What is the name of the text to the left of a command (as typed in a terminal) called?
It's called the primary prompt string, set by the shell according to the PS1 environment variable. This is usually set per user basis, for interactive shells only, (usually) defined in ~/.bashrc with the default as \s-\v\$.
On my system:
$ echo "$PS1"
\[\e]0;\u@\h: \w\a\]${debian_chroot:+($debian_chroot)}\u@\h:\W\$
and expanded to:
username@hostname:pwd$
Check the PROMPTING section of man bash to see what each token does.