This とは is a phrase used to present the definition (or important characteristics) of something (see Use of とは when there doesn't seem to be comparison). Another type of とは for surprise is not related to this sentence.
As net slang for ツッコミ, X + とは is said when some word or phrase is used in a strange and funny manner. It roughly means "Now I'm starting to wonder what X means...", "Is that what X is supposed to mean?", "What kind of X is it?", "Is that what you call X?", etc.
For example,
- A「上手にパンケーキができました!」(with a photo of a blackened pancake)
B「パンケーキ #とは」
- A「100時間勉強するだけで受かるので、とても簡単な試験でした!」
B「"とても簡単"とは」
In your example, wasn't the word ネーミングセンス used proudly before this sentence? If not, that part probably means "Now I'm starting to doubt my sense for naming things" or maybe simply "What a sense of naming!". Basically they're saying they know EK is not a very nice nickname but could not think of a better one.
((is really a punched face... It's not something ordinary Japanese people recognize. It may be a mere typo. – naruto Jan 20 '21 at 23:45((used quite commonly on some sites/forums, often in the form of 「((圧」and 「((殴」. I was under the impression that those symbolized a punched face because of articles and discussions like this and this. I understand it is obviously slang and Internet speak in origin and is probably recognized by very few outside young demographics who frequent online forums. – Eddie Kal Jan 20 '21 at 23:56