In Parshat Lech-Lecha, the Torah states (17:5): “Velo Yikarei Od Et Shimcha Avram, Vehaya Shimcha Avraham,” “And your name shall no longer be called Avram, and your name will be Avraham.” The Mishnah states that anyone who calls Avraham by the name Avram is violating a positive mitzvah from the Torah because of this Pasuk. R’ Eliezer states that one is not only violating a positive mitzvah; he is also violating a negative mitzvah because of the first part of the Pasuk, “Velo Yikarei Od.” The Gemara then asks: if this Halachah is correct, why does it not apply to Yaakov, whom we call by the name Yaakov today even though his name was switched to Yisrael? The answer is that the case of Yaakov is different because Hashem calls Yaakov by the name Yaakov even after his name is switched to Yisrael.
The Divrei Eliyahu adds that Yaakov’s name was never completely switched to begin with. He points out a hint to this in the names of the Tefilot that the Avot set up. The second letter of the name Avraham, Bet, hints to the Tefilat Boker, which Avraham established. The second letter of Yitzchak, Tzadi, hints to the Tefilah that Yitzchak established, Tefilat Hatzaharayim. The second letter of the name Yaakov, Ayin, hints to the Tefilah that he established, Tefilat Arvit. Since the Ayin in Yaakov’s name is useful, we see that the name Yaakov still had a purpose and function. This contrasts with the name Avram, which had no use and was completely replaced by the name Avraham.