The built-in default "Solid Colors" profile randomly selects a background color for each new terminal.
It works by setting the background image to a folder of images, each of which is a solid color. To choose different colors (or patterns, etc.) you can place a collection of images in a folder and set a profile to use the folder in
Preferences > Profiles > [profile] > Text > Background > Image:
Another feature of profiles is that if you create a new terminal with Shell > New Command or New Remote Connection it will look for a profile with a matching name and select that profile. It will look for a match of the entire command string, a partial match of the command name and arguments starting from the left, and it will also try to interpret the profile name as a regular expression.
This means you can name a profile “ssh” to have it selected for any
ssh command, or “ssh hostname” for ssh commands whose first argument matches hostname, for example.