During the setup I'm asked to type in my name and the computers name.
After the OS is installed, how can I know those?
Your username is usually your first name when you enter your first name and surname into the designated box during the installation process. The username is always in small caps, but at the graphical login screen your full name is shown in the default installation and you just need to remember your password. Alternatively you could also boot live media, mount the file system and look in the directory
You have to remember the password before you continue, or you would normally not be able to login. But you can reset your password.
You don't need to remember your computer name or hostname, as this is shown to you at graphical and terminal login. Unless you don't customize this, the device name of your computer or motherboard is picked and probably stripped of some numbers to look nicer and your username is added. So your computer could be named Thinkpad-$Yourname, ProBook-$Yourname, Zenbook-$Yourname if that's what you have. The hostname is defined in