Is there a period after your name in a letter?

If you are asking about your signature (as when you sign a letter), no period is needed. At the end of the letter, you sign your name in your own handwriting; and in a typical business letter, you will also type your name below your signature so that people who might not be able to read your signature will know what your name is. But in neither case is a period necessary. For example,

Sincerely yours,

[my handwritten signature would go here here]

Donna L. Halper [<---printed version of my name below it]