Utah Code Ann. § 41-1a-411 – Application for personalized plates -- Refusal authorized.

(1) An applicant for personalized license plates or renewal of the plates shall file an application for the plates in the form and by the date the division requires, indicating the combination of letters, numbers, or both requested as a registration number.
(2)
1. (a) Except as provided in Subsection (3), the division may refuse to issue any combination of letters, numbers, or both that may carry connotations offensive to good taste and decency or that would be misleading.
2. (b) The division may refuse to issue a combination of letters, numbers, or both as a registration number if that same combination is already in use as a registration number on an existing license plate.
(3)
1. (a) Except as provided in Subsection (2)(b) or (3)(b), the division may not refuse a combination of letters, numbers, or both as a registration number if:
  1. (i) the license plate is an honor special group license plate as described in Section 41-1a-421; and
  2. (ii) the combination of letters, numbers, or both refers to:
    1. (A) a year related to military service;
    2. (B) a military branch; or
    3. (C) an official achievement, badge, or honor received for military service.
2. (b) If an applicant requests a combination containing only numbers, the division may refuse the combination if the combination includes less than four numerical digits.