Messages - text - has a continuous line of text - whatever you type. No paragraphs, no subject, no signature. Some texting apps allow you to "add a subject" or keep a "signature" in the app, but that's just text that's added at the beginning or end of the text message. It's not like email, that actually has subject and signature headers.
If you were using a 3rd party texting app that allowed signatures, it updated, and the signature capability was removed, it's probably because the developers got a lot of flack about it. SMS isn't supposed to have subjects or signatures. It's like bringing a handful of water to the post office and asking to mail it.