Button rename and button behavior change refresh by itself as we close / reopen the dashboard. No need to republish the button. Auto-refresh without having to close/reopen the dashboard is required.
Having an option to enable auto-refresh after a button is clicked would eliminate some clutter (extra dedicated refresh buttons), or unnecessary clicking (dropping down the dashboard menu, clicking refresh) when a page needs to be refreshed (checkbox is checked, a filter is changed, etc.)
That said, refreshing is common enough that it really should be set to a single button hotkey, like F5 or F9 .