You only get prestige emblem 1 for a completed character. If you unlocked all your squad and complete number 10 but ignore 2 through 9, you'll get prestige emblem 2.
I've just prestiged for the first time. As soon as I finished level 60 (you have to complete this level, not just hit it, same as previous CODs), my emblem changed and I'm using the same emblem now on my second guy. I took over something like 180 points so my second guy already has my favourite class and 6 loadouts. I like this, but not everyone will. I enjoy levelling up, but having the choice to change to how I want to play as well. This can work either way if you wish.
I've updated my PPR with my prestige 1 stats.