I had a chat with a few of PvP avoiding friends and asked a question plainly: why do you avoid PvP?
The more common answer is: We can't stand the taunting and idiots in PvP who feel the need to insult.
So it's not about being competitive that makes many avoid PvP or take it as the horrible unnecessary chore to get emblems in my opinion.
Hence I am suggest this. Make all opponents in PvP anonymous. Don't display their captain or ship names. If you are in blue team, all you see in the descriptions of the red team players are their ship classes, like when you are in a DSE. Likewise for red. Disable zone chat and only allow your team to be able to communicate with each other.
Within your own team, you can see all your fellow team mates names and ships. You can chat freely and when you use /zone, it is only heard by your own team.
As for private challenges, well, in a private challenge you know who you are playing against, and in the game setup screen, you are going to get a list of players whom you are inviting. You know very well who is in it and anonymity isn't going to be an issue.