Hi
Books often have inscriptions, or the bookseller’s name.
Does "bookseller's name" mean the name of the person who sold the book, for example Mr Smith or is it the name of the place where the book was bought?
It can be either but it is usually the name of a place.
So the name of the place where the book was BOUGHT? Or maybe it means the name of the publishing house which published the given book?
The bookseller's name can only mean the name of the person who sold the book, or the name of the shop where it was bought.
Rover
I've never bought a book that carried the bookseller's name. In the US, bookstores usually provide a plastic or paper bag with handles, that carries their name. I seem to remember that in Japan, a paper bookcover was often provided with the store's name.
I have some old books that have a stamp on the inside of the cover with the name and address of the bookseller (the bookshop where the book was bought). I don't think this happens much any more.