I don't think DM is a trademark, but if you have other information feel free to provide it. Looking through older discussion forums on this topic, the only semi-definitive answer I've found is in this 2021 thread where somebody referred to a now-defunct US gov't trademark search link, where they said they found a lot of "DM"s registered but none related to D&D. I'm inclined to believe it was a working link at that time and they weren't just making shit up.

Personally I use the term DM because I've mostly played D&D, so to me it's more natural.