In effect they want to show off for their friends.And perhaps also position themselves defensively with regards to other men. It seems to me that listing a name with no hyperlink is something you could do to "fake" having a boyfriend, and thus might not be a very effective deterrent to unwanted attentions from another man. An actual FB account linked in that section is much stronger proof that a woman is unavailable, so please don't bother me.
It seems to me that if you have some significant portion of your social life online, indicators of that sort can be rather important. I know that when I was still married and could publicly portray myself as a "woman who has been married with children for a very long time" I did not have to deal with certain kinds of things in online social settings. I joined one forum after it was clear to me and my spouse that we would divorce but at a time when our status was still publicly presented as "married, with children". When I was at a point where I was ready to publicly admit I was facing a divorce, I suddenly had online social situations to deal with that simply did not crop up when everyone figured I was about as off limits as a woman could get. So my personal situation had not really changed (as I was still "facing a divorce" and not really available) but there were very noticeable social consequences when how I presented my social status changed.
I'm not on Facebook. I deleted my account earlier this year and never used it that much and I think everyone I knew on Facebook was probably either female or only interested in me due to my medical diagnosis. So I never dealt with that aspect of Facebook. But I know that I do deal with the need to signal my "currently unavailable" status in other online social settings. It's simply far easier and more effective to just make it generally publicly known that I am not currently available than to try to deal individually with every potential inquiry.
So my guess would be they are not simply showing you off to their friends. It probably serves a broader purpose similar to an engagement ring or other offline relationship status signal, and that means it may also have implications for things like what types of social invitations that single women friends might extend to them (ie "I'm no longer available for girls night out, where we go out drinking/partying" or something). Whether there is a hyperlink vs just a name listed may have hard to quantify but real impact on how others interact with them.