I almost always name my starting seven after friends of mine. It serves two purposes: 1) it gives them a personality, even if it doesn't match what the actual dwarf is like, I can at least relate to them as more than an abstraction, 2) it gives me some dwarves to keep an eye on. I typically won't nickname anyone else after the starting seven, but I'm very protective of that starting seven.
Ok actually I guess it serves three purposes, the third one being that I usually find it highly amusing when one of my "friend dwarves" dies in a typical dwarfy fashion. Then I can tell my friends they got bashed in the head and their brain crushed by a filthy trogg, fell into the well and drowned, ran in the opposite direction of the gate during an ambush, or something along those lines.
I will only really pay attention to individual dwarves when they have accomplished something fairly awesome, or brutal, or both. For example, you can see in my sig the stories of Reg, the Hammerdwarf and Atir, the Legless Hero Marksdwarf. Reg was a favorite of mine while that fort lived, and Atir, unfortunately, only became really "interesting" after (spoiler alert) his death. Both of them distinguished themselves enough that they have forever been part of my DF pantheon.
Squad leaders I keep an eye on, since they are usually the most skilled of my military, and I like to see when they get their titles.
Nobles tend to get a lot of attention, either positive or negative, depending on their demands. My current Baron is doing quite a good job of keeping himself alive. He's a Legendary cook and other than his obsession with coffins, he barely makes any demands at all.
Then there's my current King and Queen, who are both goblins. That was interesting enough that I even went into Legends mode to look them up and try to learn anything I could about them.
Also I have a Pump Operator, who used to be my Marksdwarf squad leader until he got both legs and arms shot and lost the ability to stand and grasp. Now he scoots himself around the fort, eating, drinking, sleeping and dropping bars of soap in his endless quest to take a bath. I keep thinking I should atomsmash him and put him out of his misery, but I just can't bring myself to squash someone with a dozen kills and a title just because he can't pick up soap.
So yeah, basically you have "interesting" dwarves, who get more attention from me than the rest of the unwashed masses. "Interesting" just has to be your own opinion.