One of the more interesting shifts in baby names is away from using so called 'Christian' names. One website even offers a prediction of names in 2019. It is at this link here:
They don't look like they have much Bible influence in 10 years if the guesses there are correct. This is probably fairly accurate in general, something of a trend is here. It is of course possible that our culture has just grown tired of using biblical names, but that seems too complex as a main explanation of why the trend has come about. And this ignores the fact that many names in the Bible are barely used in recent history, but could be if people were interested in the material.
The simplest explanation is normally best. And the most straightforward explanation is people don't read their Bibles, even if they do go to church, and don't turn to it likewise to name their child. And most people don't even go to church, they stay at home and watch television. Therefore, to use a cultural phrase: Out of sight out of mind.
There is another possible reason even among 'church goers.' As messages grow less Bible oriented, even those in the church probably don't come across many texts, or aren't encouraged to do so (some incidental evidence of this would be the surveys in 2007-2009 that megachurches are doing, where they find few people actually read the Bible in their ranks). Therefore they don't come across many options on Bible names, even if they profess the Bible is the main influence on their life. We might imagine on a typical week a message with ways to improve your workout or how to have a happier workplace may not touch on many biblical names beyond the obvious (Paul, John, Jesus, James, Peter, Mary, Anna, Hannah, Rebecca). And probably such messages will reuse predictable 'go to' texts once per year. The result might be that people listening also go to reuseable texts, and if there is anything to growing tired of typical Bible names, then people will look elsewhere.
The truth is I'm not sure of all the reasons why biblical names aren't used as much. But I thought I'd share some speculation, based on broader cultural trends.