It seems you can work around this by simply saying "Dave and amp semi-colon Busters" in order to get around it. It's a bit of a mouth full, but at least there's a workaround.
Not sure if joking, but presumably that then just wouldn't trigger this behaviour:
> If you happen to pronounce the name “Dave and Buster’s” as someone would normally pronounce it, almost like it’s a single word, the transcription engine on iOS will recognize¹ the brand name and correctly write it as “Dave & Buster’s” (with an ampersand).
