What drives a poor reputation for the Rogue class?

[LudicSavant]

I mean, theres a difference between lying about your name and having a false identity. A fake identity, people are greeting you down at the pub, merchants will take your credit, maybe you can get yourself an invite to a fancy/private party. Stuff like that.

Also worth pointing out, a false identity doesn't mean you are disguised. You might still look like you, which can be advantageous because people can't see through your real face, or expose your beard as fake if its your real beard. Wear a disguise, commit your crime, then take off your fake beard and turn back into Brice Lane, mild mannered playboy and new money in town, who everyone in town will vouch for being an upstanding chap.

There is a PHB background that has you start with a false identity including acquaintances, documentation, official letters, etc at level one.

And if they possessed the skills to do it once, it's reasonable to assume they're capable of doing it again somehow, especially since one of the character traits you can put on that background is "I put on new identities like clothes." Another is "I insinuate myself into people's lives to prey on their weakness and secure their fortunes."

The XGtE description of tool proficiencies says it "allows its owner to adopt a false identity." Heck, it even mentions you can use a disguise kit proficiency check to spot whether someone else is in disguise. The proficiency can represent more than just putting on clothes.