Backplate for sliding shelf; 471029
Hello! This looks like the old Merillat brand drawer socket. This hasn't been made in many years, but the good news is that you can use our 32-119 as a substitute. I've had a lot of success using this as a replacement for the very same part you show in your photos.
The catch is that you will need to redrill new holes for it to install to the back wall of the cabinet.
As for removing the old socket, these usually just plug right into the wood. However, I've known some cabinet makers who glue it in place. If that's the situation you're in then it'll be a little tricky to get out. I recommend contacting a local hardware store to see what materials they sell that would help loosen the adhesive.