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I have a maltipoo who does the exact same thing! Whenever someone comes to the house...especially if it's someone he particularly likes, he ends up gagging himself in excitement.
After talking to my vet about it, he said as long as my dog wasn't vomiting whole meals, and wasn't vomiting at any time other than when he was excited, then not to get too worried about it. Since your dog is young, he may grow out of it as he gets a bit older and more mellow with age, but more than likely, it's just the way he is.
That being said...if you notice that he stops eating, becomes more lethargic than a bulldog usually is, or vomits at other times (when not excited) then you should have your vet take a peek at him, just to be on the safe side.
I hope this helps!!