Can i use TheBookQuotes for a domain name for a website containing quotes from different books?

Is it logical? Does it imply the essence of the website?

That name is available, I find it too literal and not engaging. Why limit it to Books, why "The"

Keeping Quotes as the central concept but Quotes.com is certainly taken, consider adding some adjective, I would guess FamousQuotes is long gone as well.

InspiringQuotes
BestQuote
LastingQuotes
ClassicQuotes
BigHeadQuotes

You can paste a list like this into Godaddy Bulk Search (look for tiny link) to check availability of many variations at once.