The name told you what you could expect the technology to do. That's why it made sense to include these words in the name of email clients.
The same is not true for "Matrix".
Chat seems to be closest?
So MatrixChat might work?
Genuinely asking.
Well, that's only sensible—you're not sending an SMTP message. SMTP isn't a message format. It's a wire protocol for passing along pre-formatted messages. What you're sending is a MIME message, over SMTP. (Just like you send HTML over HTTP.)
The distinction is even clearer in the email case, actually, because those same MIME messages also show up in other transfer protocols (POP, IMAP.)
There are actually a few email clients that use "MIME" in their names. But it's pretty rare.
Conveniently, though, "MIME" is short for "Multipurpose Internet Mail Extensions", so "Mail" is actually in the name. ;)
In public communication, it almost never helps to start a sentence with "well, technically".