The title doesn't have to be the actual filename: WP automatically fills in the title attribute with the filename when you fail to provide a title yourself.
You can edit your posts, switch the editor to Text (HTML) and type more appropriate titles. Changing the titles in the Media Library won't change the versions you have inserted in the posts.
For future posts, make sure you type your own titles when uploading/inserting imges (or give better names to the image files themselves before uploading them, as raincoaster sugested).

I am having a problem with the names of my images, when my mouse hovers over an image on my live site a little yellow box appears with the name of the photo. I have not named my images very cleverly and don't want this seen, is there a way of turning it off...

Or more importantly would it be bad to turn it off for search reasons and should I rename all my images in a better way? If this is the case is it ok to do this in the media section, and go through one by one changing the title - or will this destroy any links that photo has to the website?

Thanks!
Sarah