If you look at the other types of MessagingException, you'll see the same pattern:
AuthenticationFailedException
FolderClosedException
FolderNotFoundException
...
SendFailedException
etc.
Basically, there are a set of things that can go wrong (authentication failed, folder not found, etc.) when sending a message, and the names of those conditions (AuthenticationFailed, FolderNotFound) may (initially in 1998, or even today) have come from a lower layer, possibly native code that looked like:
// Reasons for messaging failure:
#define AuthenticationFailed -42
// etc.
You certainly wouldn't expect to see "Send" in this list. You'd expect "SendFailed".
And when the failure conditions were made into exceptions, they just appended the word 'Exception' to the existing names.
That's my theory, anyway.