LAB: That’s a Remez. It’s telling us where we can find his part of the story hinted in the Torah. The Gemara is not asking for a Chumash Makor for his name.
We know that the name “Mordoch” was a popular Persian name from before that time. We know that a chief Persian god had a similar name (same with Ester). Mordechai is a Judaicization of the name. Which is what Jews have done for thousands of years (think of the name Isadore for Isaac). They have taken names similar to the surrounding nations so that they could relate when need be-but they altered it slightly to keep themselves distinct.
Ester is even clearer. Once again, we know it was a common Persian name and the name of a leading god. The Megillah even tells us she had a Hebrew name (Haddasah). This was her name that she used when involved with the Goyish neighbors.
I always find that this is so Pashut and simple. I don’t know why people get offended by this. (And then there was the one guy I met who claimed that Persians retroactively changed their histories to include these names of people and gods after Mordechai and Ester were popular.)