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When they upload an avatar in a profile you don't worry about or have control over the name.
It sounds like you want to have some control over the process. A couple of ideas, upload the pictures in the System Avatars and pick from there or let the user pick their own instead of uploading.
If you want to put them in the signature you can create a category in System Images and give registered users access to and optionaly rights to upload. You can then populate the category with pics or let them upload a picture in that category. The sig has a place to select an image or upload one for the sig.