It looks like the config set-window-option -g automatic-rename off doesn't work. When I added the following configuration:
set-window-option -g automatic-rename off
set-option -g allow-rename off
in /usr/share/byobu/profiles/tmux, automatic renaming was turned off.
/usr/share/byobu/profiles/tmux
from: https://stackoverflow.com/a/51910118/8025086