Knacks

I definitely think it's presented for a reason. In my opinion, Kvothe actually has a "knack" for naming. The most explicit example being with the Horse, Keth-Selhan. Kvothe doesn't even mean to name it for what it is, but he does - One Sock.
It's pretty suggestive he does the same thing when he names Master Ash. Denna is a bit taken aback, but in the end agrees to give him this name. In my and many other fans opinion, likely because the name fits her patron well.
Undoubtedly his naming of Auri, as well, is very fitting. It never does say what Auri actually means, but the reaction we recieve from both Elodin and Auri in regards to her "new name" is very telling.

I also feel that Elodin accepting Kvothe into his naming class is pretty suggestive that Elodin see's this quality in Kvothe as well. At first Elodin is reluctant to admit him because, Kvothe is pretty reckless and really doesn't think everything through, adding an ability such as naming to his character could potentially be dangerous, not just for Kvothe, but for bystanders. However, that evening with Auri, Elodin discovers that Kvothe is in a way, wildly naming things without any constraint whatsoever, which is probably a lot more dangerous than if Elodin instructed him on harnessing that power to be used at will. So Elodin goes with lesser of two bad ideas and allows Kvothe in his class.