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.

As an agent my comments do not constitute the practice of law, but another good guideline is the Bilski "machine or transformation test," in which it can be shown that the invention is the algorithm tied to a computing machine specifically configured to store and execute the steps of the algorithm, you've got a good case (machine,) or if you can describe and characterize data in a "before" state, then describe the structure of the data in an "after" state after the algorithm has done its work, and then show that the difference between these states (transformation) represents a useful improvement (utility.)
The converse of this guideline, similar to Mr. Lau's remarks is that any computing process which you can complete entirely in your head is very likely NOT patent eligible. In re Bilski, the rejection of that algorithm reads: "...the invention is not implemented on a specific apparatus and merely manipulates [an] abstract idea and solves a purely mathematical problem without any limitation to a practical application, therefore, the invention is not directed to the technological arts."
So, include some of the elements that the Bilski rejection is lacking, and you may have something you can own and protect.