Need help integrating script with logged in users

I have a golf website that I have recently added a handicapping system to and now need to incorporate this fully with the WordPress user that is logged in.
You can see it in use here https://publicaccessgolf.com.au/handicap and you can see the two files it uses here https://pastebin.com/5m7M79b3.
I have also set up the required db table called golfhcapu and it is all working fine. It is saving the data and retrieving it, so all good.

I am wanting, instead of the user entering their name, it will automatically be entered for them when they are logged in and then all of their games and handicap are saved so that when they log back in, all of the info is there for them.
So basically I need the script integrated fully with the wordpress user system but I’m unsure of how to go about this.

Any ideas are appreciated