call me crazy, but shouldn’t the mothers at least know the names of the guys they are sleeping with?
I wholeheartedly agree. However, in reality that isn't always the case. There is also a serious issue of if the mother doesn't want the father to know that they had a child together.
If he refuses to go through with the adoption and gets custody of the child, she would likely have to pay child support. If she gives the child up for adoption she can get reimbursed for medical expenses and possibly even for time off work up to a certain amount (I'm not very sure about how that works). She also relinquishes her parental responsibilities to the adopting couple.
I don't mean to belittle the sacrifices a woman makes when they decide to have a child out of wedlock and to give that child up for adoption. However, if a woman chooses to do that, there are incentives for her to not tell the father about the child.