As to how common it is, well, that depends. It's common enough that I've seen it on one system or another at almost every place I've worked as an SA.
But it's perfectly fine, and
[username]@[domain] is simply the fully qualified username. Much like a server on a domain is often shortened to
[machinename], even though its name is really
[machinename].[domain], user names are often shortened for the sake of brevity and expediency. The
[domain] part is implied between people and (where necessary) explicitly provided behind the scenes, transparently to the user.
I would personally look at seeing if I could drop the domain bit off the end, because it is a little bit of an inconvenience, but I'd weigh that against how difficult and risky the change to do so would be, and I'd factor in the length of the domain name too. I worked at a company with a 19 character domain suffix once, and I made sure I didn't have to log in anywhere by explicitly providing the suffix pretty quickly. I've also worked at companies with 3 letter domain names, and for something that short, I generally didn't bother unless I was desperate for something to do.