Merch, you say?
*adjusts glasses*
Whatever you choose to do I HIGHLY recommend this series by Nerd City on Merch and Merch Design.
I have some things to say. From what I've seen on merch for Furry content there basically three 'tiers'. Easy, merch that's "cheap" and simple but don't provide a high level of "brand display"; your key chains, pins, stickers, etc. The Medium is the kind has a balance of price and display, probably items you'll make the most on; shirts, SFW Posters, etc. And finally the Hard tier, the tough sells, high brand display and quality but high price; Dakimakura, NSFW Posters, etc.
Now how would that fit into MinoH? I'm glad you asked.
1. Easy - As I said stickers of chibi version of the staff, and even memes are on the table, important items like the laurel and the lyre could also work. Keychains could work with the different backgrounds the player can pick as well as the important items. I suggest making it not too explicit that these items are from Minotaur Hotel; doing so can entice buyers the aren't comfortable about having furry merch on them.
2. Medium - That the shirts you can have Asterion wear can be made into merch, so could the Hotel uniform. It would also be nice to get a poster or postcard-like-thing featuring the characters in isolated/non-canon scenarios.
3. Hard - Dakimakura is pretty straightforward, right? You could have them feature the Asterion in different colors, then based on the popularity of that expand to the other staff members. What I said isolated/non-canon scenarios pics also applies here; naughty-style.
That's what I have to say. I WILL get merch if it does become a thing. And I ain't gonna lie, it'll be mostly to support all of your amazing work.
Happy new year, everyone!