After changing your name, you are required to notify Driver's Services.  Note, you are NOT required to actually obtain a new driver's license within 10 days.  You are only required to NOTIFY Driver's Services in writing of your name change.  Because individuals who are transgender and who are changing their name may face discrimination or unpredictable results when attempting to change the name and/or gender marker on their driver's license, they are advised to seek legal counsel.

Title 27 - Transportation
Subtitle 2 - Motor Vehicle Registration And Licensing
Chapter 16 - Driver's Licenses Generally
Subchapter 5 - Administration Generally
27-16-506.  Notice of change of address or name.

Link to Statute: Title 27 - Transportation (LexisNexis website for Arkansas Code)

Text of Statute:

Whenever any person after applying for or receiving a driver's license shall move from the address named in such application or in the license issued to him or her or when the name of a licensee is changed by marriage or otherwise, such person shall within ten (10) days thereafter notify the Office of Driver Services in writing of his or her old and new addresses or of his or her former and new names and of the number of any license then held by him or her.

An application submitted by a licensee to change the licensee's name on the licensee's driver's license must be accompanied by the original or a certified copy of one (1) of the following official documents that provides evidence of the change of the licensee's name:
A recorded marriage license;
A court order;
A divorce decree; or
Any other document, including a document issued by the Department of Homeland Security, that is deemed to be satisfactory by the office as evidence that the name change is in accordance with state and federal laws.