Is there a name for the final section of a letter?

When writing a letter it typically starts out "Dear..." and then has the content, then before you sign it you might have a formal or informal (depending on who you're writing to) sign off, for example:

blah blah blah letter content blah blah.

Kind regards/Many thanks/Best wishes/Cheers!/etc

Does this final closing portion of your letter have a name?

For comparison, the middle portion of the letter is the body and the opener could be described as a greeting or, more accurately, the salutation. but I don't think this last bit could be called a farewell as such.

So what should it be called?

I have always heard the "Sincerely, Joe Smith" part of a letter called the closing.

(And the part you describe as the greeting ("Dear Mr. Blahblah") I'm used to calling the salutation.)

It's called a valediction or a complimentary close. The opening phrase is called a salutation.