Under certain limited circumstances, a US trademark registration can be amended. Such an amendment is called a Section 7 filing. An amendment to the mark itself is only permitted if the amendment does not materially alter the character of the mark. 37 C.F.R. §2.173(d). Whether or not a change is a “material alteration” is not always a simple question. A Section 7 request could also be used to delete or restrict the description of goods and services used in connection with the registered trademark (which is often advisable if some of the goods or services are no longer in use by the registrant).
For example, I recently amended my registration for TM4SMALLBIZ.COM to TM4SMALLBIZ. The amendment was accepted. The deletion of the .COM is not really significant as .COM is treated like other very common wording with little or no trademark significance, such as “THE”, “A”, “INC” and “LLC”.
I filed for the amendment because the domain registry for the new .XXX domains was refusing my sunrise application to block any TM4SMALLBIZ.XXX application filed by anyone else, contending that my trademark registration did not match the portion of the domain to the left of the “dot”. I disputed their analysis, but in the end it was easier to file the Section 7 amendment.
Below I have included the entire Section 7 filing made with the USPTO.
For more details about the requirements for a Section 7 filing, see Trademark Manual of Examining Procedure (TMEP) Sect. 1602.
Can you add a name to a character in a trademark?
I can’t comment on the specifics as I haven’t seen them, but that would not likely be allowed. It would likely be best to file a separate application to register and protect the character.