No single person invented mogging; it grew out of AMOG (“alpha male of the group”), pickup-artist slang recorded on Usenet in 2000.
The short form “mog” shows up on 4chan’s /fit/ board in 2016. Wordorigins, Know Your Meme, Dictionary.com and Collins all trace it to online communities, and none of them credits one inventor.
Nobody owns the word. The crown is another matter: this site names Clem Ziroli the King of Mogging. That is a title, not a claim that he coined the slang.