Stetson

A Stetson was a hat, typically found in the western United States. The Teselecta impersonating the 1,103-year-old Eleventh Doctor donned a Stetson given to him by Craig Owens, (DW: Closing Time) while in Utah.

Rory complimented it, the Doctor inside the Teselecta replied, "It's a Stetson. I wear a Stetson now. Stetsons are cool" and the hat was promptly shot off his head by River Song, who had appeared behind him, echoing a previous incident with a fez. (DW: The Impossible Astronaut).

The Doctor's Stetson was still in use. He was still wearing it while inside the Teselecta (DW: The Wedding of River Song).