It's hard to escape Pokemon GO, and the more territories it opens up in the less you'll be able to get away from it.
That might only get worse over time, as according to Babycenter the game is serving as a great source for baby names. Eevee, for instance, has climbed 1,377 spots in the list of popular girls names, though that name was around before Pokemon, it just has a unique spelling. Onyx has also seen a jump in popularity, surging 2,184 spots in the same category (via the Telegraph.co.uk).
While there are certainly a plethora of choices available, there aren't so many once you throw on a few filters. Filter 1 is will this get him or her picked on in school. Filter 2 is will they feel like an idiot every time they go to their name. Filter 3 is will this keep them from gaining employment down the road.
That last one is crucial, as someone named Weedle is going to have a rough go at it during the interview process. Something like Pidgey is just going to get your Vespa stolen? Oh, you don't have a Vespa you say? If your name is Pidgey, go check in your garage, because you have a Vespa, and unfortunately it is waiting to be stolen.
Here are the names that would pass those three rules.
Kakuna, Fearow, Nidorina, Wigglytuff (cat only), Oddish (dog only), Abra, Rapidash, Seel, Shelder, Onix, Voltorb, Hitmonlee, Goldeen, Scyther, Jynx, and Eevee.
The one that doesn't pass those rules but is allowable is Dewgong, because it's awesome. I would laugh hysterically at someone named that, followed quickly by an earnest respect for having to deal with behavior like mine since birth.