(Nothing canon, all my own campaign.) I've been assuming identity is proven by papers from a character's homeworld. New cards for the same identity would be issued in Imperial service, from a new homeworld on changing residency, and even on employing with a megacorp (specifically including Mongoose's Merchant Marine career), so you could acquire two or more proofs of the same identity.
identicard or implanted chip
Chip only from high TL, high law level worlds, otherwise card or passport. Duplicates available for a fee and with a hassle at your homeworld or consulate.
Banks will also take great care to verify identity, not just checking ids alone but doing background checks and querying embassies/consulates before making large loans, especially including starship mortgages. You're very unlikely to slip a fake id past them on a mortgage, meaning it's very likely your real identity tied to it.
TAS would probably also be invested in determining real identity for their members, both paid and awarded.
I can think of multiple reasons why a character would change identities. The most obvious is a criminal past, but they could be fleeing from personal threats, family vendetta, crippling debt, political or religious persecution, etc.
Desirable, but not easy. Without knowing technical details, I just assume authorities wouldn't laugh it off or make it easy - anything PCs can think of, NPCs can think of. So it'll be technically difficult; still possible, but a big deal.
Some polities might make it easier to get new identities, either deliberately or as a consequence of other policies. But IDs from those polities would also be subject to greater scrutiny. Like traveling on a Jackson's Whole identity in the Vorkosigan universe, if that's not too obscure. Might get you flagged for further attention, even as it gets you through.
Another consideration is "legend" - a footprint of work history, life history, passport stamps, online presence, etc. Even a convincing id might raise red flags for a serious investigator if it's too clean and new.
In the Traveller universe Social Status might tie into legend. A fake identity as a knight or better might be subject to greater scrutiny than one as a belter. Maybe it passes all technical tests at first, but if no-one's ever heard of him someone takes a second look. A belter's id might escape that level of scrutiny, but also wouldn't get you in as many places.
It's a little meta-gamy, but in Mongoose, by analogy to the spending limit on gear before play starts, if you've come out of character creation with enemies, or terms in a Rogue career, I'd say that's all tied to the identity you start play with. They've got the name you're using now, quite possibly the name of your new ship. Forging or buying one after that should be barely possible, but also difficult enough it's not a free clean break in the first session.
