A cafe in the new Mary Brück Building and another in the refurbished Roger Land Building will open mid-2015.
The College of Science & Engineering is running the competition, with two £100 Amazon vouchers awarded for the winning entries and coffee vouchers for runners-up.
There are no restrictions on suggestions but names reflecting the College's work are encouraged. Head of College and Senior Vice-Principal Professor Lesley Yellowlees will make the final decision.
Entries should be emailed by 12pm on Monday 2 March.