When I traveled to Shikoku and visited Dogo Onsen, I had the chance to stay at Funaya Hotel in Matsuyama. It is where the Emperor and Crown Prince have stayed when they visited also. The hotel was a nice mixture of old and new architecture.
Dogo Onsen was about 10 minutes walk away and as I went out dressed in yukata to head towards the baths, I was given a small carry basket (bucket?) with a towel in it. The tag on the basket says “funaya” ふなや for Funaya Hotel. Some others in the street also had this baskets with their own hotel names on it.