“you can TRY to trademark ANY phrase. Whether you are successful is another matter.”
Copyright was the term the other poster used, not trademark. There is a difference.
How do you copyright a phrase? It’s not a book or a song.
TEA Party would be a trademark, not a copyright.
Or at the very least, it would be DBA (Doing Business As).
But establishing ownership (not just use of) requires further action.
Bands experience it all the time, several bands using the same name in different local markets. Then both start to record and one gets some exposure (distribution, tour, etc.) and they battle it out in court to see who established first.