ST Voyager "In the Flesh":
CHAKOTAY: Let's just say it's good to be back. What about yourself? How long have you been posted here, Mister?
BOOTHBY: Boothby. Boothby's the name.
CHAKOTAY: Boothby. I've heard of you.
BOOTHBY: I should hope so. I've been tending these grounds for fifty four years, give or take a few months.
CHAKOTAY: And beautiful grounds they are.
BOOTHBY: Mmm hmm. Logistical Support. Straight through the main complex, second door on your right.
CHAKOTAY: Thank you.
BOOTHBY: Commander, Logistics is a secure area. They won't let you in with that holo-imaging device. Fresh from the Neutral Zone? You're not a Romulan double agent, are you, son?
CHAKOTAY: Actually, I was just recording a few images for my friends back home. Would you mind posing for a shot?
BOOTHBY: Me? You want a picture of me?
CHAKOTAY: The one and only Boothby. My friends would be impressed.
It's clear from the dialogue above that Chakotay has never met Boothby before, or pretends not to know him.
ST Voyager "The Fight":
EMH: That's right. Try to remember more about the holodeck.
CHAKOTAY: I was sparring with a Terrellian, and Boothby was there. He used to train me when I was a cadet.
EMH: Keep going. What round was it?
CHAKOTAY: Three. Round three. The fight was going badly. I was avoiding my opponent.
[Holodeck - Boxing programme]
(And back we go into Chakotay's memories of a slightly grubby gym.) BOOTHBY: Stay away from the ropes, son. That's it, that's it.
COMPUTER: End of round three.
From the above dialogue clearly Chakotay knows who Boothby is/was as he was trained by Boothby to box when he was a cadet.
Somebody might say that he was trying to trick the aliens, but what purpose would it serve to do that? Maybe playing ignorant so he wouldn't get caught? But it really seemed like he didn't know Boothby when he met him at the aliens training facility and one might argue that not knowing who Boothby might actually raise suspicion since he was the groundskeeper at Star Fleet Academy for 54 years.