How did the town of Truth or Consequences, New Mexico get its name?

It was the result of a radio show contest.

In 1950, the town decided to rename itself after the "Truth or Consequences" radio show, having formerly been known as Hot Springs.

Host Ralph Edwards had said he would broadcast the program from any town renaming itself, to commemorate the show's tenth anniversary.

It was the beginning of a relationship between Edwards and the town, with annual visits over 50 years, along with a series of events collectively known as Fiesta.

https://en.wikipedia.org/wiki/Truth_or_Consequences,_New_Mexico