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I'm partial to something like "network wonk" (wonk is always a kind of funny term) or "network czar". Terms of royalty have a nice air of pretense about them, such as "Earl of Rackmount" or "Duke of Renderfarm" or "Baron von Webfarm".

Try some foreign words. The Brits always have some good slang you can steal from, although "Cable Wanker" probably isn't appropriate. Or Yiddish: "Computer Maven" (or just Maven) would be all right. "Computer Maven to the Stars" is even more grandiose. Made-up German like Computerische Obergruppenfuherer might be amusing to the right people.

Look at stealing from TV or books: maybe you want to be the "Dell Whisperer", "Clicker of Mice", "Robotic Overlord", or "Speaker To Computers". "Nick Burns, your company's computer guy" would make the SNL fans laugh, although it'll mean nothing to anyone else. Maybe some title from Harry Potter would be good: "John Smith, Defense Against the Dark Arts and Server Maintenance."

In general, long titles can be funny: "Chief Systems Infrastructure Architect and Mouse Clicker", if that's your thing. Or you can adopt a new nickname, such as John "Where's the Any Key?" Smith, or John "Reboot!" Smith. You could think small, such as "Mouse Tamer" or "Mouse Wrangler". "Keyboard Jockey" is bland but wouldn't be inappropriate.

Alliteration is OK, although you've got to do better than my lame example of Chief Computing Consultant (C^3).

Just remember: you'll likely get sick of anything after a while, and don't pick a nickname that you won't want to be called.