Creating website with many images for seo purpose

I have a website with 1000's of images.
My question is that if the website is about animals, and i have multiple categories like elephants, horses and dogs and i create a new post for each category which have atleast 10 images each.
Should i than call the images as this : elephants images 001 , elephants images 002 , elephants images 003 or would that be bad for seo.

Your naming convention looks fine for SEO, but I would be more concerned about the website itself. Sounds like its heavy on images with little or no text content. This could put you at a disadvantage. Another thing is you probably don't want to have several images on each page because that will lend itself to slower page loads which is a big ranking factor. Maybe you can do one of those slideshow style sites that have been really popular lately. You know you might have a post like "10 funniest elephant images" and then you will have a slideshow with 10 individual slides and each slide will also have some text content for SEO. I see these pages a lot lately and I don't see as many thumbnail galleries etc. as I did in the past.