Then there's the band "The Postal Service" that got a cease and desist from USPS to stop using their trademark.

However it had a happy ending: the United States Postal Service -- the real one, as in stamps and letters -- signed an agreement with Sub Pop granting a free license to use the name in exchange for working to promote using the mail. Future copies of the album and the group's follow-up work will have a notice about the trademark, while the federal Postal Service will sell the band's CD's on its Web site, potentially earning a profit. The band may do some television commercials for the post office.

[1] https://www.nytimes.com/2004/11/06/arts/music/postal-service...

For the longest time I thought these were the same companies

Or Uninteruptable Power Supply. When I got my first job, I always wondered why our company designated the UPS with their own room on the floor map...