On December 10, 2009, Google applied for a trademark on the Nexus One name, but it looks like they’ve been rejected:
https://gizmodo.com/google-applied-for-nexus-one-trademark-5427455
The application was refused because of “likelihood of confusion” with an existing trademark of the word “Nexus”, which was registered by Integra Telecom, a telecommunication services company, in 2008.
Google’s intending to challenge this decision and will “continue to claim rights to the Nexus One trademark in the United States.” [Geek]
