In the absence of market research, here are my immediate thoughts on ways to make this work:
Try to find some of the Tooheys New tv ads (Australia) - they're currently promoting themselves as "the official currency of the beer economy", which is basically what you're talking about - beer as thanks.
Payment system will need to be easy - even things like selecting a beer and writing a note might make it too hard, so offer 'random' selections of premium / boutique / foreign beers and random selection from a page of sample thank you notes (these would be short, funny, grateful, and blokey - the sort of page I might share as a link even if I don't use your service).
I think thanksbeer, thankbrew etc are all good. Something incorporating 'Cheers' could be nifty, as Cheers means both 'thank you' and 'bottoms up'. Cheersbeers.com?
I wonder what restrictions / limitations you encounter selling alcohol over the internet?
Definitely not part of the MVP, but being able to login and create my 'wish list' would be awesome. Then when a mate says 'I'll get you some beers' I could say 'Go to Thanksbeer, look me up and it will give you some ideas'.
Having 'different' beers is probably critical. I assume it would be cheaper for me to buy a friend some beers locally rather than use your service for the same brand, but I'll gladly pay a premium for a beer I've never heard of or tried before.
And final thing which is relevant to all business planning - how much gross margin can you realistically make? (Say, a couple of bucks per beer? $10 per carton?) How much do you want to make from this (Say, $5000 per month)? And then is it realistic, and if so how do you, go about building this so you can sell 500 cartons a month?