There can be an economic rationale to almost any decision, including those decisions that involve obtaining information. Reading your question, I would start by comparing the utility from knowledge with the utility from surprise. So long as utility from knowledge is higher than the utility from surprise, individuals will prefer to know. This behavior is consistent with rationality.
Empirically, I doubt that many individuals derive much utility early purchases or an early choice in name. (Most of the urgent stuff is gender-neutral anyway, afaik) However, there may be psychological benefits to obtaining this information before childbirth. For example, individuals might want to adapt their expectations.
This could be a behavioral story. Consider a two period scenario, where the first period is the decision to learn and not to learn, and the second period is the childbirth, where you learn anyway. Also consider that the individual derives utility from the difference between their expectations and the outcome. (Such a utility function is behavioral, because the net utility is dependent on not just the outcome, but the expectations.) If the individual is uncertain about their decisions in period two, they might want to set their expectations under risk averseness, or not learn if they are risk-lovers. It is just an idea.
With this line of thinking, one behavioral model to research might be Rabin and Koszegi (2006) "Personal Equilibrium".
If you would like a model with no behavioral component, that might be a bit trickier. Intuitively, we could expect more knowledge to generate more utility than less knowledge in general. However, this does not always need to be the case. If there is a commitment mechanism to commit to "not knowing", this could potentially have some returns for the parent. (I am not sure whether this can be convincing. I am more convinced by a more behavioral story.)