They obviously knew what they meant, but how much did they think about that meaning? My original thought, though, is did anyone ever get mocked for their name, especially if the name is far more war-like than they are?
In that case, this may be of help to you. It's a thesis published looking at Old Norse nicknames. some of them are superbly uncomplimentary.
If you look at the Icelandic Sagas you can see some interesting nicknames; there's Skalla-Grímr, which means Bald Grímr. His father was called Ulf, but his nickname was Kveld-Ulf, wich means evening wolf. The thesis goes into more detail about how and why people got their nicknames.
Well some of names of famous viking characters they themselves took on at some point, mostly middle names or last names like Blåtand, Trätälja, Lothbrook, Järnsida. You can almost say that those circumstantial "last names" are more like titles or nicknames. And ofc some names where given to them in hopes of providing a certain trait, like animal names, Björn (Bear) or Ulf (Wolf). If we take the name Trätälja (trä=wood, tälja=carving/working with wood), that name is from Olof Trätälja a Swedish viking king that moved to the region of Värmland after his father, king Ingjald Illråde, was killed. When in Värmaland he started to cut down the trees and making the land more hospitable. As this was not considered to be an appropriate thing to do as a lord or royalty, he got the name Trätälja as an insult/bad nickname by other lords and people. And this is the only name we know him by. I do not know, but I would think that if a known coward and weak person (physical and psychological) would take on a name like "the great" "dragonslayer" or whatever they would be challenged. Who wouldnt want to beat a "great" or a "dragonslayer" in a duel? So I believe they where a bit careful with that.
I also want to point out that there are no archeological evidence that Trätälja really existed. He is mentioned in Ynglingatal and Heimskringla.