omeir davar b'shem omro

The gemara (Kiddushin 54a) records a discussion that took place in the Bais Medrash reported by R’ Avin and adds that R’ Nachman did not hear whether this report was said by R’ Avin bar R’ Chiya or R’ Avin bar R’ Kahana – he simply heard stam R’ Avin’s name. The gemara asks what difference knowing the speaker's exact name makes, and answers that it is relevant in case a contradiction is found between the report and a statement by one of the other R’ Avins - is it really a question, or do we have the wrong R' Avin?

Why does the gemara not consider knowing the exact name of the speaker significant because of the need to be “omeir davar b’shem omro”, to give credit to the source of a statement? If when Esther reported the plot to assassinate Achshveirosh in the name of Mordechai (the source for omeir davar b’shem omro) Achashveirosh had thought she meant Mordechai the shoemaker or Mordechai the tailor instead of Mordechai his advisor, I imagine events might have taken a different turn.