The easiest option for me was to rename the title of the terminal instead. Please see: https://superuser.com/questions/362227/how-to-change-the-title-of-the-mintty-window
In this answer, they mention to modify the PS1 variable. Note: my situation was particular to cygwin.
TL;DR Put this in your .bashrc file:
function settitle() {
export PS1="\[\e[32m\]\u@\h \[\e[33m\]\w\[\e[0m\]\n$ "
echo -ne "\e]0;$1\a"
}
Put this in your .tmux.conf file, or similar formatting:
set -g pane-border-status bottom
set -g pane-border-format "#P #T #{pane_current_command}"
Then you can change the title of the pane by typing this in the console:
settitle titlename