What do you call afterthought in a letter?

There isn't a specific term for an afterthought in a letter. However, you can use these phrases:

Formal:

* P.S. (Postscript)

* Addendum

* Note:

Informal:

* P.S. (Postscript)

* By the way...

* Oh, and one more thing...

Example:

* Formal: "Dear John, ... [Body of the letter] ... Addendum: I forgot to mention that I will be out of the office next week."

* Informal: "Hey Sarah, ... [Body of the letter] ... P.S. I'm so excited to see you at the party!"

Ultimately, the best option depends on the tone and formality of your letter.