If this were my project I would create a different comp for each name by simply duplicating the comps in the Project Panel then changing the name. I would remove the background video, duplicate the comps, change the names, then render each title using the Render Cue or AME using the Lossless With Alpha preset. The rendered titles would be brought into PPro and added above appropriate shot in the sequence.
If you have CC 2014 I would work differently. I would create a Text Template in AE for Premiere Pro. This is a much more efficient workflow. Here's how: How to create text templates in After Effects for Premiere Pro | Adobe After Effects CC tutorials
Thanks Rick. Yes I'm on 2014 and text template does sound perfect as I might want to refine the style of the text and change the animation after creating the individual titles. I don't suppose it's possible from a single composition to bring in part of it above the video and part below it while retaining a single composition? I can easily create a comp of the background animation and just align it with each title clip and presumably that's also a dynamic link back into AE so if I change it there, all instances in PP will change. But if there's a smarter way of doing this from a single composition I'd be pleased to hear how.