They are expecting a number of humorous suggestions, so please do get involved and who knows, it could be your name printed on the side of our new vehicles!
The best three names will be selected by the force's Dog Section, so get your suggestions in by April 30.
To enter email: [email protected]
The competition follows on from the successful naming of PD Billy who was chosen by kids in the QMC children's ward last year.
Supt Steve Cartwright said: "We had great success with naming PD Billy at the end of last year; we thought we would ask the general public again to help, this time naming our new vehicles for the Dog Section.
"We're all looking forward to seeing what suggestions come in!"
The force is also offering a prize to the chosen winners to visit Force Headquarters, meet the police dogs and see their chosen suggestion on the cars.