You need some kind of editing application to add titles or names to a video. AE makes videos. There's nothing else you need to do. Just give them a high quality render of your work and let them worry abou it.
If they don't know what they are doing, then they will have to pay someone that does to do the work for them.
But what kind of editing software would you suggest?
I will like to give them options....
Depends on what they are doing with the movies and what kind of computers they have. You Tube can add captions, Movie Maker or iMovie can do the job. Premiere Pro, Final Cut, Vegas, Avid . . . and about a zillion other apps will edit movies. The level of sophistication and the price point depend entirely on what you're trying to do. Without more detail I can't give you a better answer. You might as well ask "Why did this blue?"
If they just need to add logos and text I would suggest one of the consumer programs like imovie, or the Adobe Elements software.
Photoshop now offers basic video editing capabilities too.
Editing video is not possible with Photoshop Elements.
Photoshop Elements is for photo editing
In order to edit videos , you should use Premiere Elements or Premiere Pro
However, Adobe does offer a combined package of Photoshop Elements and Adobe Premiere Elements, which might work perfectly for someone who just needs the most basic tools for editing both photos and video.
If your clients just want to stick with one program then they could Buy a normal license of Photoshop, but it'll cost a lot more. As Andrew said, you can import, export and edit video files and it has a Timeline window for basic video editing:
However, the choice is going to depend on their budget. Photoshop is $699 for a full license whereas the Photoshop Elements and Premiere Elements bundle is $149.99. This Buying Guide illustrates what you can do with the Photoshop Elements and Premiere Elements bundle: