While I do agree it is way too early to decide how many Sou sent the pictures to (let alone the girls in class possibly taking pictures for themselves), they could be getting hearsay from whatever social networks the girls have.
I know you said you get the need for Sperm Centers, but this allows me to go on a mini-dive, so apologies in advance:
Sure, the sperm centers are a small personal quandry, but on a scale of Societal Ethics are basically required to have any functioning population. Every woman would need to have at least 1 child (and obviously 1 of them needs a 2nd) to keep population stable. Factoring in a subset that will not have any children due to personal reasons, and a scattering number of men who cannot contribute due to being infertile, you are looking for closer to 2 children each.
If the men, primarily viewed as shy and woman-hating, were to follow stereotypes and not be mandated to deliver sperm regularly, population would plummet. There is no mention of women being incentivized to give birth (I know another series similar in nature mentions governmental stipends for childbirths), but the mandate isn't meant to be unnecessarily cruel to the men.
Think about how labrynthian it comes to trying to keep first generational incest to a minimum when it seems widely accepted that each Sister and Mother of a male is expected to be their first wives. I'd also imagine to increase genetic diversity women not in a harem situation basically are subtly enforced not to have the same father for any child baring the occasional twins or more. But this is supposition from out sample size of 1 family and schoolgirl rumors, so this is taken with a liberal spoonful of salt.
So sure, it is a bit weird to have children without your (as the sperm donors) consent, but you also aren't expected to raise them either in the case of donations. Honestly given how things work, and the relative scarcity, names have to be removed in case of the 20+ women you possibly got pregnant try to contact you for your own safety. Imagine the nightmare scenario of someone like Hinata's mother accosting you just because she could track down you for giving her Hinata.
I'm actually curious if in universe you need to get dna tests or if you can walk up to a sperm center or a hospital and just ask if your sperm donors match, like seeing if your dad was #D254C (possibly batched out as well, wonder if manual/non-official sperm center conception has a special tag).
