How can I protect and monetize an algorithm?

No pure algorithm can be patented per se but the applications of that algorithm can (if novel and passes non-obvious+inventiveness tests), and also the implementation under copyright. Getting it named after you is a matter of convincing people that it is convenient label ... however it is more social proof (outcome of brand) rather than a registered property right. Afterall people think google because they type it in hundreds of times a day and repeatedly mentally bombarded with that name. However, an algorithm is usually buried in the guts of code and thus why should a user care whether it is bubble,quick/etc sort.

My suggestion is that if you crave the limelight, keep on inventing more algorithms and be known as the go-to-guy (read book brand-named-me) on that particular domain.