Hi. This is a great question! (Probably why no one has yet to step up.). In order to infringe a copyright, you must have access to copyrighted material and have something substantially similar. In short, you have to know about it, and copy it. Trademark is different. You can infringe without knowledge. If "Z" has trademarked his moniker, there could be an issue. However, in my humble opinion, I do not know how he would quantify damages. Just having a nickname does not give rise to TM protection. It must be used in commerce on some type of goods or services (Like if he had "Z" t shirts). Hope this helps!
Intellectual Property laws are both broad and complex. Every case rises and falls on the specific facts of the case. One thing you will find that holds true, however, is that the law in general will not allow someone else to profit off the name, reputation, and goodwill of another. Ask yourself, "would I be mad if someone else did this" or worse yet "would I be on the phone to my lawyer if someone else did this?" If the answer is yes, then there is a good chance that the other person will be on the phone to their lawyer.
At the end of the day, if someone is profiting commercially from someone else, then there is generally going to be some form of remedy available. Intellectual Property lawyers can generally figure out a way to explain the harm and seek the appropriate remedy. Sure, there are lots of defenses like fair use in copyright and the like, but anytime you are doing something to trade off someone else - then you are probably at risk. The question then becomes - as my colleagues on this site have suggested - whether someone is going to enforce the rights and how much in the way of "damages" is at stake.
Probably not legal. This would violate the right of publicity and possible right privacy of the person whose nickname is being hash tagged. Further, the nickname might also be a protected trademark, and this could constitute trademark infringement.