For the first month, it really doesn't matter, really. Furniture is the same, car seats the same, clothing, sure, but you can buy that any time and does not require planning. And as it regards names, just have agreed upon two options, one for each case.
Or just find out because it doesn’t matter either way? Or don’t. I wanted to know for both my children. It didn’t make any difference, but I still just wanted to know because I could and was curious.