Info on framing for someone that knows nothing about framing

I want to know what the ‘paper’ part of the frame is called and if customizing that part is possible to do at home or if I’d have to have it professionally done by a framer.

Ive collected a few vintage frames so that part is covered, but I’d like to use bold colors for the picture cut outs and do interesting shapes as well similar to these examples. Is it possible to buy the supplies to do it myself? or what should I ask for if I go to a framer to have it done.

Any extra info is welcome! Thanks