This thread is a few years old, but the correct answer is to change the value of the variable that holds that information.
If you modify the git-prompt.sh script a bit (for me, this is located in c:\Program Files(x86)\Git\etc\profile.d\git-prompt.sh), you can make the title anything you want.
Note: You will need to run VS Code, Notepad ++ or similar as administrator to write back to this directory.
PS1='\[\033]0;$TITLEPREFIX:$PWD\007\]' # set window title
PS1="$PS1"'\n' # new line
PS1="$PS1"'\[\033[32m\]' # change to green
PS1="$PS1"'\u@\h ' # user@host<space>
PS1="$PS1"'\[\033[35m\]' # change to purple
PS1="$PS1"'$MSYSTEM ' # show MSYSTEM
PS1="$PS1"'\[\033[33m\]' # change to brownish yellow
PS1="$PS1"'\w' # current working directory
example:
...
PS1="$PS1"'STACKOVERFLOW@ABC ' # user@host<space>
...
PS1="$PS1"'LOL ' # show MSYSTEM
...
console:
STACKOVERFLOW@ABC LOL /
$