b4nny I told them that he should simply switch his ESEA name to phlps to be eligible or FULLY COMMIT to the name Happycool across the board so that it reflects his "proper" alias. This would likely entail changing aliases on other platforms to Happycool and insisting on people calling him by Happycool to be convincing. For that day only he used the name Happycool on Twitch, asked TFTV to switch his name in the article, etc., so it seemed he was on board with making it consistent. At this point it seemed they would be eligible. Shortly after, however, he disregarded all of that and continued to use other names and never insisted to be referred to as Happycool. This is where they lost eligibility.
He had his name changed on pugchamp to happycool, used it in the faceit cups, and had the tftv article use it as well. Nowhere in the your ambiguous rules does it say anything whatsoever about needing to match with discord, twitch and tftv. You claim he 'disregarded all of that' by continuing to use other names but it's clear that he made a conscious effort to be consistent across the board where it matters: i.e., in esea, faceit tourneys, tftv articles, even pugchamp. What does your discord alias have anything to do with esea league fee reimbursement? The same goes for posting on the tftv forums, and twitch, they are in no way official. Even if they were relevant, do you seriously expect them to be able to read your mind and know that esea/pugchamp/tftv official articles isn't sufficient for a 'proper alias'?
I changed my alias on esea from kkktookmybabyaway even though I've used that alias for literally 4 years, but even still my alias is not the same across the board (tftv forum name is bearodactyl, pugchamp is bear, tftv article just says bear, etc.). There's plenty of other cases where people don't have matching aliases between esea and tftv as well, triplemint for example is tripbwai on esea, trippa on the forums, and trippahaha on pugchamp.
You also say "he never insisted to be referred to as Happycool" despite these efforts he made, do you really expect him to correct every single person in pugs who calls him phlps? My teammate, Pete changed his name from knuckles across the board and plenty of people still call him knuck, is this somehow his fault if he doesn't care to correct it every time? It definitely seems like you are just drawing arbitrary lines to try and get out of paying them.