Does one write:
Smith toshokan or Toshokan no Smith
Apologies for not using kana, the Windows' Japanese keyboard is taking forever to install.
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When I lived in Japan, all the libraries I came across were Name+Library. For instance, 京都府立図書館 or "Kyoto Prefecture Library."
"no" indicates possession. Toshokan no Smith would mean "The Library's Smith." Smith no toshokan would be awkward (and I think incorrect, at least based on my experience) but would mean Smith's Library, which at least makes sense.