Fortunately I don't decide the team's schedule!
Randomly selecting a name from a pre-defined collection can be done in 10 minutes, and it can be done in a day, depending on requirements and constraints. I don't pretend to know the guys' schedule, but IMO it's always good to have features requests known.

His suggestion is wrong exactly for the reasons I've stated - you can't really tell players to alt-tab and go to a different website to select a name. Of course I can do it, but it's not good UX at all.

And yeah, I can think of a name of my own, but having a Random option is always very nice and comfortable (and potentially funny). Just like games add a Randomize Looks button - of course players can design their own characters, it's still sometimes fun to let the game "create" them.