As in like Lucy, Wendy, Natsu and all, their edolas friends had the same name. How come, then, that Makarov and Gerrard were different? There are official sources (can't remember where I saw that) that their Edo-characters were named "Faust" and Mystogan repectively. What makes these 2 different than everyone else, whose Edo-name was the same? (Natsu, cana, lucy, elfman, sugarboy, hughes, coco, etc.)
I think that is a plot hole. The thing is, there is no way everything can be opposite in Edolas. Like you said, Faust really is Makarov and Mystogan really is Gerrard, but in Earthand Makarov is not the father of Gerrard. You assume that the names are coincidences for everyone (even that is very unlikely) and do not forget that some characters were not so different in Edolas, like Gajeel. They were very similar in personality, and also Coco seems very similar in both cases. (Note: Earthland Coco was a filler in the anime. Along with Sugarboy, Hughes, and Byro)
Also, remember how in Fairy Tail Battle with Laxus Natsu and Gajeel were for some reason considered "over 80 years of age"? Well the reason for that is revealed up ahead in the plot, which is that:
They are actually over 400 years old. Including Wendy as well.
If you see things this way, there is no way Edo-Natsu (or Edo-Wendy or even Edo-Gajeel) would have been there when Natsu, Happy, Wendy, and Carla visited Edolas, since we are sure that with Edo-people, they don't have the same circumstances as the actual Fairy Tail members.
In Conclusion: I think that is an unplanned mistake; unless it is intended, but say if Gajeel, Natsu, and Wendy weren't in Edolas then that would raise a question too early, since the answer is revealed quite a long time after. Perhaps Hiro had to make things that way.
Jellal's Edolas counterpart is named Jellal.
He says in chapter 167 "My name is Jellal" to Wendy. Mystogan is a fake name.
As for why Faust is not named Makarov, that could probably be because of the different birth situations. The idea for the name Makarov came because he was born to one of the founders of Fairy Tail and Mavis named him (Chapter 450). However, Faust was never related to the Fairy Tail guild, so the Edolas Mavis wouldn't have a chance to name him. There's a reason why he isn't the guild master.
Since someone else named him, his name is different.