I've noticed another user that's using an identical Display Name to mine. Is there a protocol for dealing with this on SE or am I expected to just suck it up?
Duplicate usernames are not seen as an issue on the StackExchange website.
This has been discussed previously
People have the same names in real life. Isn't StackOverflow real life?
If they didn't, and people missed out on their first choice, you'd be left with trying to come up with all sorts of variations just to "be yourself".
You don't want it to be like AOL or Xbox Live (badges notwithstanding) where if you're not the first, you're docsavage1933 while some other joker, who just happens to be in before you gets to sit around on docsavage
Regardless, the chap who shares your username has been on the stachk exchange network since '09, and on sci-fi since '11. Please don't see this as a case of him copying you, or taking some individuality away.