The names of the beaches came from the offices of the commanding generals, so Bradley's staff named Utah beach and Omaha beach. Exactly why those names were chosen is unknown. The fact that they match the letters of the naval task forces: U-force and O-force is probably not a coincidence. And in some early references Omaha is referred to as Oregon. So the idea of picking short state names that matched the forces involved makes sense. Ultimately why Oregon was changed to Omaha is unknown.

Quite interestingly there is a story from a man who served in Bradley's office as a carpenter, Gayle Eyler. He claimed that Omaha was named for him. He came from Omaha and evidently was a fixture around headquarters having coffee with Bradley from time to time. So the story goes Bradley named the beach after him, and Utah after another enlisted man named "Sam" from Provo, Utah. The Omaha World-Herald tried to track down "Sam" a couple of years ago, but couldn't find anyone who matched the name and description, which makes Eyler's memoirs a bit questionable. In all the story has to be considered unconfirmed. I only mention it because it has become a popular version of the story, and thus needs to be debunked, or at least questioned.

I'm less familiar with the British beaches. Hopefully someone can say why Monty chose those names.