what was the name of long john silver's establishment?where else was that name found?

The name of the establishment was the Spy-glass. I'm not sure what the second part of your question is asking.... please advise.

WHEN I had done breakfasting the squire gave me a note addressed to John Silver, at the sign of the Spy-glass, and told me I should easily find the place by following the line of the docks and keeping a bright lookout for a little tavern with a large brass telescope for sign.