You know where you press enter to look at the Dwarf traits[1] and another key to see the relationships? Press (IIRC) 'y' instead to get to the nickname and profession (re)-naming options. The key is shown clearly on the screen as a hint, if it isn't that.
Or, use Dwarf Therapist and right-click on the dwarf's row-header (their name) and you get the chance to apply said nickname. (Even more powerful, as you can't (easily) put certain characters from DF, but DT allows you to set them easy enough. You can also group dwarves by whether they have a nickname or not, although I don't think you can sort by the nickname (BICBW), which might have its own uses in addition to all the other grouping/sorting options.)
You might also want to change the appropriate part of the INITs if you don't want
Firstname Lastname changing to
'Nickname' Lastname but would prefer
Firstname 'Nickname' Lastname or similar, instead. (DT has the latter format, IIRC, so making it the same in DF makes cross-comparing lists easier. But that's only a fairly trivial reason to change it, and doesn't apply if you don't even
use DT.)
My hints about nicknames. *Urist 'SCr15Crp5Mas4' McWhatsit" can be descriptive (albeit likely to be out of date when he does some more carpentry/masonry) and useful for organising, although in that case it's a little long, but it looks horrible in the "This is a masterpiece carved by..." description. This is something I used to do. These days I just give nicks based on their one primary (or
intended primary) skills. Urist 'Soapy' McSoapworker, Urist 'Sapper' McMiner, Urist 'Harrison' McCarpenter[2] or even Urist 'Psmith' McSmith when I'm feeling playful.
But that's beyond your original enquiry, and I'm sure you already have something in mind.
[1] And, if you don't, it's the last of the 'screens' from the character viewing selector, or ?v? (the non-zoom viewing option, my fingers remember it when I'm there, but it also says at the bottom of the screen) from the Unit list).
[2] Well, I used that not-so-obscure reference once, when I had used 'Chippy', 'Planker', and several others also as carpenters in that fort. And given there's no archaeologist/smuggler/replicant-killer jobs in the fort (yet!), I felt I could use it safely enough without confusion...