Typically, it's common practice and advisable by most state boards to have the license and seal match. This ultimately avoids confusion in the event audits are conducted, plans reviewed, etc.
I absolutely agree, when in doubt use what is on your license. Texas does however allow for the use of middle initial:
137.31(d) All seals obtained and used by license holders shall contain any given name, commonly accepted variation of the given name, or initial
combination with the surname as currently listed with the board and in the usual written signature. Nicknames shall not be permitted on a
seal in lieu of a given name or initial combination. The name can be displayed on the seal using all uppercase letters such as "LESLIE H.
DOE" or using the standard combination of upper and lowercase letters, such as "Leslie H. Doe". If after licensure, a license holder legally
changes his/her name, the license holder must have a new seal or seals made showing the new legal name and submit an imprint or imprints
of the new seal(s) to the board for review, approval, and processing (submitted within 60 days of name change).