You will need Bloodline or higher to be able to chose your surname. I would guess choosing to be a ward isn't an obstacle to getting that custom surname as long as you have that tier.
The way it will work for nobles and aristocrats according to what the devs said in Discord is that they get to choose their family in their chosen starting settlement, that family will get ranked up accordingly. The player can then use their surname token to give themselves or their whole family their pre-validated surname.
I'm sure it won't be too different for other starting points, the tokens can be used at any time - but you do need Bloodline tier as a minimum.