I tend to vary it a bit depending on the rating myself.
1-2: Random name.
3-4: GM picks a common name for you NOT John Smith or similar ones.
5-6: pick a specific name for yourself with GM approval.
My reasoning is if your just buying the low levels then you get what your given the fixer's not going to really care if your a blue eyed, blond haired man with the name Apunda Dong because any proper check is going to burn it anyway. Its just a quick and dirty thing to dodge automatic checks and pop up a "Valid" result.
In the mid-range your paying for a reasonably solid ID so they'll go "here's what we've got that match's your requirements" it wont be a perfect match but it'll be close e.g. the blue eyed blond could be Lars Nilsson it'll stand up to a bit of prodding but a determined check will still find its not you. However they avoid the names that are too common e.g. introducing yourself as "Dr John Smith" will get most people reacting with a "Really" because its too generic a name and will actually stand out a bit more in their minds than Bruce Campbell or Don Kojinski. Their not as bad as introducing yourself as "Sparkleface Vlad Kingdong Mahukabak" but they will draw a bit more attention than a less common name that sort of fits.
At the top range the ID's are customized to fit you near perfect match's for biometric data, detailed histories, etc and I just don't see a fixer conveniently having that on hand so you can just walk in, pay and walk out. You need to give them time to pull strings, adjust histories and insert the correct data into the new ID for you. that kind of expensive purchase and detailed existence is going to be custom designed to match you and for that kind of price having the fixer set it up with the name the client wants makes sense to me. Maybe its a private, cover identity where they want a name that will register with them. Maybe they want a specific ID to pass as Lord Borg of Mlakistan as part of some bizzare plan and the very name itself is going to be an identifier to their contact. Either way there isn't going to be an identity that match's at a lvl 5/6 range just sitting around for them to buy they will need to wait for it to be created. The GM approval is less of a "You name is stupid and you can't have it" than it is a "This would put the fixer at risk so they're not going to make it".
