Jidgetbones re I don't like this idea of naming a primary parent, anyway, as surely it's an equal partnership in a lot of cases.
I think the legal side of which parent takes more/the most time off is a legal issue but generally my experience of parenting is that it is not 'equal' in terms of time. I've experienced this with both my birth child and adopted child and I only personally know of one couple who literally shared equal parenting time. So for me, my dh worked full time and I had a year of adoption leave off from my part time job, and now work part-time, with our adopted child (and 8 month maternity leave with our birth dd previously).
Where I think this is more relevant with adopted children is that they sometimes bond more with one parent first, and then through that connection they can bond with the other parent. We were told about this and I can certainly say have experienced this with our son (now 5, we've known him almost two years).
In our son's case he was more attached to his birth mum than birth dad, and more attached to the female foster carer of the couple and then I had the time off with him so it seems quite easy to understand why he would attach to me first.
It has meant that we need to consciously share out care when dh is around because, for example, my son will often ask for me to do the story and bath. In the early days we did allow him to chose what made him comfortable but then we started to say dh woudl do it as he had not seen ds all day! It can be quite hard for both parents when the child has a preference (I know because my birth dd had a preference for daddy when she was younger, but she kind of grew out of it). I think with newly adopted children it has to be handled carefully because it's not as straight forward always as 50%/50%, but of course if people have found it is straight forward for them then that is great.
For other children things may be totally different.
I am saying this because I think it can explain why social services like parents to nominate who will be the primary carer. I think in the OP's case things may be different if they are both around equal amounts of time, but as I say I have not experienced this. (In general as I know tons of parents where mum is at home more than dad, one family where dad is around more than mum and one family where they did genuinely share care of the kids 50%/50%.)
Good luck KumquatMay hope the adoption leave all works out well.