Well unfortunately for Shrink Fan, they probably won't be able to enforce their trademark on their name alone. For the reason Doll-Elf mentioned. The name is simply too generic. The funny thing is that the company behind Shrink Fan and the affiliated something...fan sites, kinda proof this with their own naming convention.
Shrink Fan
Giantess Fan
Expansion Fan
Muscle Fan
Vore Fan
Metal Fan
Bondage Fan
Transform Fan
Futanari Fan
Monster Girl Fan
All of these names are a relatively generic term with the word 'fan' behind it, thus likely non enforceable as a trademark on their name alone.
That being said, Doll-Elf could easily use a slightly different name for the Discord server. You wouldn't want to have a generic name as Shrink Fan associated with your Discord server, right?
(;
(for people who would like to read the law themselves, here is a link)
https://www.uspto.gov/sites/default/...ents/tmlaw.pdf