Unless they changed it really recently, that's just not true. Like AmericaDelendaEst, I only use old.reddit (and i only use reddit if I absolutely have to or if I'm in the mood to troll/spread leftist agitprop and subsequently get banned) but I've tried account creation on regular web reddit and old.reddit and in both cases it let's you choose your own username. It always automatically suggests a pre-made autogenerated username but you don't have to choose it.

For anyone who wants to agitate on reddit and also stay truly anonymous, here is an excellent guide to doing so from @marcie@lemmy.ml

https://hexbear.net/post/3789920