Bulk edit media file Titles (not file names) or have them match their parent

I’m not sure if this is the right section to post this in, but I’m hoping the functionality is already possible somehow, probably in the form of a plugin that I’m unaware of.

Here’s what I’m trying to do:
I have a bunch of images, and by default when they are uploaded the File/Title becomes what was available in the exif data, or it’s simply the name of the file itself (IMG_20130127_115403.jpg -> IMG_20130127_115403)

I want to be able to select images in the media library, (or have this be done automatically if the image is uploaded to a page/post) and have their titles match whatever post/page they’re attached to, their parent, or more simply enter in a new name manually and update those media files with the new name.

The end result would be me being able to change a bunch of images titled “OLYMPUS DIGITAL CAMERA” or “IMG_#######_######”, to whatever their parent is or my own custom name, e.g. “2013 Assorted Photos” or whatever.

It would also be great if it updated the slug too, but ultimately the important bit would be the title.

—

Main reason I’d want this other than SEO reasons (alt tags) is when using lightbox or similar galleries, and you have the Title set to show… it shows the random media titles that were given to it either taken from exif or taken from the file name, and with the ability I’ve described above it’ll result in titles that match what the photos are actually about, and if I want to include a custom title or “caption”, I can edit individual images and write out the custom description of that image.

For most images though, just having the title match the page title / gallery title / post title, whatever it’s attached to, would be sufficient and save me a lot of tedious editing.

—

If anyone has any idea how this might be achieved, or anything similar such as a plugin that simply allows me to batch rename the titles (I’ve seen plugins that let me rename the actual file names, but not the titles that wordpress uses in the database), I’d greatly appreciate you pointing me in the right direction.

Posting this thread because my own searches have come up short. I’m a bit new to wordpress so I’m hoping someone with more experience will be able to help me out.

Thank you in advance!