I change the name of one of my campaigns somewhat regularly (about weekly), and it's very inconsistent if the changed name will be visible when viewing the characters in that campaign. I changed the name over a week ago, and while it's visible on 4 of the 5 characters, one of them is still showing the campaign's previous name. Occasionally it'll be even more behind than that, with a character showing the name from 2 weeks before.

I have experience this recently.

I changed my campaign name, characters made before the change seem to hold onto the old title, new characters have the new title. 

Hmm, that makes sense. It must only check for an updated campaign name when the players edit their character, and most of them probably only do that when leveling up.

It should update the campaign name for character sheets when you force a data-cache update: by either changing their level (as noted; you can bump them up a level then back down), or by clicking the Inspiration box twice and then reloading the page. (Changing their subclass or race would also force an update but it's best not to just for this reason.)