There is not a specific name to the feature.
However, the phone I am referencing holds 1000 contacts (and allows you to put up to 7 numbers into each contact) on its phone memory and an extra 250 on the SIM chip (a feature of AT&T).
I am not exactly sure how many pictures the phone holds, because it is just stored in memory of the phone. However, it gives you 25 MB of space in the phone, while the average picture is about 20-30 KB. I did the quick math and figured, if you just want photos in your phone, you can store about 800-900 photos in the phone. Then, if you do decide to get the extra memory chip, you would have an extra GB of space to do whatever you please (whether that be put even more pictures, songs, videos, etc.)
I just switched two weeks ago from Verizon to AT&T and I could not be any happier. My phone plan is so much cheaper now, and I am able to do so much more with my phone. My old phone only held 60 pictures.