I absolutely adore the name Verity!
So, I do think that some people will think of the novel/film since it has been so prolific on social media in recent years. However, it’s a very “of the moment” association, and I honestly don’t foresee people thinking of that association for the majority of her life. Sort of like Hazel after The Fault in Our Stars, where I’m sure a lot of 2013 parents of baby Hazels were reminded of the reference, but even just a year or two later, the reference was monumentally less prolific, and I’m positive no Hazel gets that these days. Or if they do, it’s quite rare.
Verity as a novel itself will definitely not become something like Carrie or Juno. I also don’t foresee it drastically rising in popularity. A slight uptick, perhaps, but nothing too crazy.
If this name ends up being The Name for baby, please don’t let this stop you from using it! I truly don’t think the reference will be an ongoing issue.