At the beginning of this week's Parsha, Hashem introduces Himself to Moshe using His four letter name, known as the Tetragrammaton, which consists of the Hebrew letters that correspond in sound to the English letters Y,H,V, and H שמות ו:ב'(). Because of the sanctity of this name, the proper practice, when referring to Hashem's name, is not to even call these letters by their usual names, but to say "Yud Kay Vov Kay" instead, as noted by the Chayei Adam (כלל ה' סעיף כ"ז). Hashem then tells Moshe that although He appeared to Avraham, Yitzchak, and Yaakov, He did not make Himself known to them by this four letter name, but by another name (שם פסוק ג'). In his commentary to the Torah, Ibn Ezra (שם) points out, citing examples, that the Avos were indeed familiar with this name of Hashem, but their understanding of its significance was incomplete; the Ramban (שם) concurs, adding that the Avos did not have a clear comprehension of this name, since they did not know it though prophecy.
The Rambam, in his Moreh Nevuchim (חלק ב' פרק ל"ה), uses this very Posuk (שם) to document the fact that Moshe's level of prophecy was greater than that of the Avos, presumably because prophecy came to Moshe via this name, and not the less important name associated with the Avos. Earlier in his Moreh Nevuchim (פרק ס"א חלק א'), the Rambam explains that this four letter name, unlike other names of Hashem which are descriptive of a specific attribute, in fact represents the very essence of Hashem, and hence His transcendence, and perhaps signifies His absolute existence. The Tur (אורח חיים סימן ה') writes that this name describes the eternal nature of Hashem, indicating that He was, is and will be; the Shulchan Aruch (שם סעיף א') records this idea as well. The Baal HaTanya (ליקוטי אמרים תניא, שער היחוד והאמונה פרק ד') adds that this name indicates that Hashem is the source of all that exists, and he explains later (שם פרק ז') that it also indicates that Hashem exists beyond the realm of time and space. The Rambam (שם) points out that this name is often called the Sheim HaMeforash, meaning, the distinct and exclusive name; it is the name applied exclusively to Hashem.
It is worth noting that Rav Chaim Volozhiner, in his Sefer Nefesh HaChaim (שער ב' פרק ב'), writes that even this name of Hashem does not fully describe the very essence of Hashem, but rather describes His relationship with His created universe; he refers in a footnote there to a statement found in Pirkei DeRabbi Eliezer (פרק ג',ועיין שם בפירוש הרד"ל אות י') which suggests this too. Nevertheless, the Sefer HaKuzari (מאמר ד' סימן א') writes that there is no name of Hashem more precise and significant than this four letter name, which is His private and exclusive name. The Gemara in Sotah (דף ל"ח.) points out that this is the name referred to when Hashem speaks of His own name (שמי), meaning, the name which is exclusively His (as in במדבר ו:כ"ז, among other places). Based on a Posuk elsewhere in the Torah (שמות כ:כ"א), the Gemara (שם) explains that for this reason, this was the name of Hashem used in the Beis HaMikdash. There, it was pronounced daily by the Kohanim during the Birchas Kohanim, as documented by the Mishnah in Sotah (דף ל"ז:-ל"ח.), and ten times by the Kohein Gadol on Yom Kippur, as stated by the Gemara in Yoma (דף ל"ט:). The Tosafos Yom Tov in Yoma (פרק ו' משנה ב' בד"ה כשהיו) quotes from Rav Moshe Cordavero that the exact pronunciation of this name was different on Yom Kippur than it was daily during Birchas Kohanim.
Commenting on that Posuk in the Torah, Rashi (לשמות שם בד"ה בכל) indicates that the Beis HaMikdash was the only place where this name could be pronounced, a point noted in Tosafos in Sotah (דף ל"ח. בד"ה הרי) as well. The Mechilta (פ' יתרו, פרשת בחדש פרשה י"א) formulates an actual prohibition to mention the Sheim HaMeforash outside the Beis HaMikdash, as does the Gemara later in Yoma (דף ס"ט:); the Rambam (פרק י"ד מהל' תפילה הלכה י') rules accordingly. The Gemara in Kiddushin (דף ע"א.) derives from another Posuk in the Torah (שמות ג:ט"ו) that Hashem wants His true name to be hidden, and the correct pronunciation of this name was thus taught only very rarely and only to very worthy students; the Rambam (שם) codifies this as well,explaining that this was done as a sign of honor. The Gemara (שם) also notes that even in the Beis HaMikdash, those Kohanim who knew how to pronounce one of Hashem's names would do so only when other Kohanim were singing, so that others would not hear it and learn its pronunciation. The Gemara earlier in Yoma (דף ל"ט.) states that after the death of Shimon HaTzaddik, the Kohanim stopped using the Sheim HaMeforash during Birchas Kohanim; Rashi (שם בד"ה מלברך) says that this was because they felt unworthy, while according to Tosafos in Sotah (שם), this was because the Shechinah no longer rested upon the Beis HaMikdash to the same extent. In either case, the use of this name appears to have been generally discontinued even in the Beis HaMikdash, as the Rambam (שם) again states. The Rashash in Sotah, commenting on the aforementioned Tosafos (שם), points out, though, that it continued to be used as part of the service on Yom Kippur. Based on the Yerushalmi in Yoma (פרק ג' הלכה ז', דף י"ח:), the Rambam (פרק ב' מהל' עבודת יוה"כ הלכה ו') writes that during these later years, the Kohein Gadol pronounced the name in a very low voice so that others would not learn it. Once the Beis HaMikdash was destroyed, of course, the name was not used at all.
The Mishnah in Sanhedrin (דף צ.) lists among those who have no share in Olam HaBa one who is הוגה את השם באותיותיו, meaning, he pronounces Hashem's name based on its letters (and vowels). The Gemara (שם דף ק"א:) explains that this refers to saying the name outside the Beis HaMikdash and in a disrespectful manner. Rashi (שם בד"ה ובלשון) writes that the precise violation here is either pronouncing the name using vocalization from a language other than Hebrew, or pronouncing and explaining one of Hashem's other names in an inappropriate setting; pronouncing it in the normal Hebrew manner, albeit outside the Beis HaMikdash, does not, in fact, result in such a terrible punishment. In his Peirush HaMishnayos on this Mishnah in Sanhedrin (פרק י' משנה א'), however, the Rambam writes that the prohibition is to pronounce the Sheim HaMeforash with the letters as they are written; the Bartenura, in his commentary there (שם) agrees, although the Tiferes Yisrael (שם אות י') raises some questions. This prohibition is precisely explained in Tosafos in Avodah Zarah (דף י"ח. בד"ה הוגה) to refer to pronouncing the four letters which make up the Sheim HaMeforash as one would normally pronounce these letters (and vowels) should they appear in another word; the Rosh in Yoma (פרק ח' סימן י"ט) explains it this way as well. The Chayei Adam cited above (שם) rules that this is the Halacha.
The Ri is then quoted in that Tosafos (שם) as holding that one shouldn't even say the letters "Yud" and "Hay" (together) because that too spells out a name of Hashem. As explained by the Maharsha in his commentary on that Tosafos (חידושי הלכות שם), the Ri's position is that it is not only forbidden to pronounce the Sheim HaMeforash, but it is also forbidden to state the names of the letters (sequentially) which make up that name. The Radvaz (שו"ת הרדב"ז ללשונות הרמב"ם, חלק ה' סימן ל"ה) writes that although the accepted prohibition is to pronounce this name as it is written, the opinion of Tosafos (שם) that even to state the names of the letters is forbidden actually is more in consonance with the simple language of the Mishnah in Sanhedrin (דף צ.) which refers specifically to letters; he thus rules that this too is indeed forbidden when referring to the Sheim HaMeforash. The Chayei Adam (שם) accepts this ruling as well, as noted above, saying that when one pronounces the spelling of the Sheim HaMeforash, one should say "Kay" instead of "Hay." The Chasam Sofer (שו"ת חתם סופר השמטות, חלק חושן משפט סימן קצ"ב) writes as well that people should be careful to do this. It is worth pointing out that according to Tosafos in Sukkah (דף ה. בד"ה יו"ד) and in Shevuos (דף ל"ה. בד"ה באלף), the prohibition to pronounce these letters is violated only if one's intent is to refer to the name of Hashem; one should, however, be very careful with these letters in general.
For this reason, Rav Ovadyah Yosef (ספר ילקוט יוסף חלק א',הלכות ק"ש וברכותיה, הערה ל"ו) quotes that those whose practice before performing a Mitzvah is to recite "LeSheim Yichud," the text of which mentions the letters of the Sheim HaMeforash, should alter the pronunciation, either as described above, or by inserting a word like "אות" (letter) in between each letter, as suggested by the Ben Ish Chai (שנה ראשונה, פ' וישלח אות י"א). The Noda BeYehudah (שו"ת נודע ביהודה מהדורא קמא חלק יורה דעה סימן צ"ג) writes that although he thinks in general that one should not recite "LeSheim Yichud," if one does, there is no problem mentioning the letters of Hashem's name in that context. Rav Ovadyah Yosef (שם), though, cites those who hold that there is a textual error in the Noda BeYehudah, and it is indeed improper to recite those letters in order at any time.
It should be noted that since we do not pronounce the Sheim HaMeforash at all today, whenever we come across it (in Davening, Kerias HaTorah, and so on), we substitute another name of Hashem, Ado-nai, as indicated by the Gemara in Pesachim (דף נ.), and explained by the Mishnah Berurah (או"ח סימן ה' ס"ק ב'). The Vilna Gaon (ביאור הגר"א שם בד"ה ויכוין) notes that when the Sheim HaMeforash happens to be juxtaposed to the word which is normally pronounced Ado-nai (based on its own letters), we substitute Elo-him for the Sheim HaMeforash. The Yalkut Shimoni (חלק ב' רמז תתמ"ג) states that because we don't know the Sheim HaMeforash today, our Tefillos are not always answered; in the future we will know it and all our Tefillos will be answered.