Regarding the name that others see when you call them.
Caller ID Name is not sent across the POTS network (landline or cellular), only the Number. For such calls, any Caller ID Name that the callee receives is generated by the callee's phone service provider by doing a database lookup on the Number. There is no single, universal, master database. No guarantee that the correct name will be against your number in all databases. Not a lot you can do about that.