Yes, but when they go to buy that name, should it be chosen by them or from a list.
That is all there is to this question, nothing else about the system.
Well in case of FOnline its debatable since the community is not that large therefore its possible to keep things up and running using premade gang names.
But when it comes to game itself you can see that often gangs don't care what name is on the TC line. They call themselves otherwise anyway and they are referred to as "own gang name" rather than "premade gang name" here on forums too. They only had to take whats left ingame so they could setup a gang.
Therefore I've mentioned other aspects of 2238 that are closely connected to gang names and affect each other.
base = gang
-> can end up in 1 gang using 3+ other gang names just to have more bases
more bases = more gang names
-> need to create new gang names when all premade are already taken
So far everyone starting an active gang has 2 options. Either choose from premade name and be recognized as such or simply ignore premade names and call themselves as they see fit and with enough propaganda, community will memorize and call them by their own name, not by the premade one. And so far my experience is that those who participate in wasteland politics choose to ignore premade names. And I must say there have been no attempts to go down in history with gang name like "Pwned ya n00b" as far as I can remember. Also there is another sort of people who don't give a f*** and for those gang name is just another requirement to get place for few people to safely store stuff and play a bit together.
So for big gangs or people who want to be seen its a great opportunity to create their own identity ingame. And for everyone else, well... that name won't be seen by a mans eye until next wipe, when some dev might decide to read them in database, so where is the harm in this?