I’ll start with one of each: Dick Trickle and Major Frank Burns.
Vitas Gerulaitis.
Coach Dick Crum
Drogo Baggins.
Primula Baggins.
Mungo Baggins.
Bungo Baggins.
Basically, 80% of the Baggins family tree.
Fyvush Finkel. (But I guess if you’re Jewish, that might sound ordinary.)
Wally Cox
In one of Agatha Christie’s Poirot stories, with David Suchet, Poirot is visiting an old friend who’s a doctor. The office secretary, who doesn’t know Poirot and is confused by his “foreignness” walks in to the doctors office and announces that there’s a man outside suffering from “Hercule Poirot”.
Lemony Snicket.
From The Orville: Bortus. Don’t know what it is, but if you have it, stay near a toilet.
Foghorn Leghorn sounds like a highly exotic tumor of some sort. (I don’t think the more native-Italian-sounding Fovorno Livorno has the same problem. :))
I looked at a list of Dickens characters, thinking i might find some there. I didn’t, but one of them stood out for another reason: John Baptist Cavalletto is described as “a small time Italian smuggler”, and I thought “If for some reason I had to smuggle people, I would not want to have to start out by smuggling Italians.” 
Fanny Craddock.
(She used to have a cookery show on U.K. television in the distant past)
Bioroids from the Appleseed setting. Their species name sounds like something you go to a doctor to have lanced or cut off from some sensitive area.
“I can’t sit down, I have bioroids.”
Phillip K. Dick(the first stage of Wally Cox).
It’s never Peter Lupus.
You’ve contracted Dinklage, you’ll be a great actor but very short.
Peter Dinklage-Much worse.
Keeping with the show theme I would hate to contract Coster-Waldau Disease.
Going the other way, have you heard of that new Country Music star Braxton Hicks?