If a member of the general public submits in writing that they find a specialty plate objectionable the complaint is reviewed and a response is sent. (Three such complaints were received in the last year.)  Although it is infrequent, TxDMV has required a customer to obtain a new personalized license plate. An example, a personalized plate was taken out of circulation as a result of a law enforcement alert regarding gang references.

The department’s objectionable criteria provide a consistent way to review personalized plate applications and keep potentially offensive plate patterns off the road. There is no limit to the creative expression on personalized plates.

Verifying availability may be done online at either TxDMV or My Plates’ Web sites. If the response is "unavailable," it means the plate number is already taken or has been declined. 

Resources:

Texas Administrative Code 217.28

(C) Personalized plates not approved. A personalized license plate number will not be approved by the executive director if the alpha-numeric pattern:

(i) conflicts with the department's current or proposed regular license plate numbering system;

(ii) would violate §217.22(c)(4) of this subchapter as determined by the executive director; or

(iii) is currently issued to another owner.

Texas Administrative Code 217.22   

(B) The executive director finds that the alpha-numeric pattern may be considered objectionable or misleading, including that the pattern may be viewed as, directly or indirectly:

(i) indecent (defined as including a reference to a sex act, an excretory function or material, or sexual body parts);

(ii) a vulgarity (defined as curse words);

(iii) derogatory (defined as an expression of hate directed toward people or groups that is demeaning to people or groups, or associated with an organization that advocates such expressions);

(iv) a reference to illegal activities or substances, or implied threats of harm; or

(v) a misrepresentation of law enforcement or other governmental entities and their titles.

(C) The alpha-numeric pattern is currently issued to another owner.

Texas Transportation Codes:

504.002 General Provisions

504.005 Design and Alphanumeric Characters

504.0051 Personalized License Plates

504.101 Personalized License Plates

504.102 Personalization of Specialty License Plate