I name them when I catch them on cam often enough to be familiar, and they have an identifiable rack, which is usually around 2.5yrs old. Every named buck is monitored by charting cam and personal sightings with date, time of day, location, and weather. I follow them as long as they use my property or they're dead. Could be months or it could be years.
Naming them allows me to keep track of them without getting confused or overlapping info. After a season or two I have enough info on an individual buck to reasonably predict where he likes to be at certain times and certain weather patterns. On the macro, I learn about the property as a whole, how it's used by bucks generationally.
The names are merely an identifiable label. If I call a buck, "the big 8", the name could apply to any one of a dozen or so bucks. By giving them a name I know one 8pt from the the other 8s, and so forth.