We got a 1 star review that's clearly meant for a different business

Before you reply, check the name against your customer records properly. People use nicknames or a partner's account, so now and then the "wrong business" review turns out to be a real customer. Better to find that out before you say publicly they never came in. If it really is a mix-up with a similarly named business nearby, expect more of them. Making sure your name, address and photos are clear on the profile helps cut down on that.

Report it from the reviews section of your business profile and pick the option about it not being relevant / not about this business. That's the category Google actually removes for, so it's a better shot than flagging it as fake. It can take a few days, and Google has a review management tool where you can check the status and appeal if they leave it up. Meanwhile reply to it publicly, short and polite: you can't find any record of them as a customer and think it may be meant for another business. Future customers reading it will get it, even if it never comes down.