How is it possible these two players have the same nickname? https://bf4db.com/player/391231689 and https://bf4db.com/player/1957844232

Certainly they are not the same account because of different EA GUIDs but belong to the same person because were used with the same IP (joined our server).

I'm aware if someone changes his nickname another player can pick the previous nickname. But these guys have the same name at the same time. Any thoughts? Glitch/bag?

EA wonky DB design. Not going into details how it works, but it is easily done. Can be on purpose or by accident.

Can't check the two you linked as I am on my phone but they could also be XBOX or PS accounts. Those can have the same name as on PC.

Battlelog shows they are PC only accounts. 

http://battlelog.battlefield.com/bf4/soldier/Schlampentraum73/stats/391231689/pc/

http://battlelog.battlefield.com/bf4/soldier/Schlampentraum73/stats/1957844232/pc/

It's interesting that these two links (PC bf4 soldier profile) above have unique numbers to distinguish the accounts whereas the account profile 

http://battlelog.battlefield.com/bf4/user/Schlampentraum73/

has nickname only as an unique identifier. Thereby we can open only profile page of the 140lvl guy