Hello!
There's a lot of flexibility about this, but your character's name is important in some cases. For one thing, it has to be unique, so you'll be cautioned in character generation against picking a name that other characters already have.
You are free to introduce yourself by any name, and if that other character RECOGNIZEs yours by that name, it'll work like your name for them. If you're wearing a disguise they will have to recognize you again. It's possible to try to live a double live as two different people wearing different disguises and introducing yourself by different names, but it may catch up to you at some point due to things like bank accounts and lodging records, which end up having to be in your real name... for now. We haven't yet implemented forgery skills but it's something eventually on the horizon.
The way things currently work, couriers will have difficulty delivering to the homes of people whose actual names they don't know. And, it's also possible to try to figure out someone's name by asking around about them through the rumor system.
This is really a great question and it's possible some of these answers will change as we go on, but there should always be changelog notes regarding big shifts like that.