How to set a fixed title for a terminal in Mac?
Open the Preferences for terminal app
Select the profile in use
Select "tab" pane on the right
Uncheck everything except Show activity indicator




Repeat the above for Window title if you want that to change in addition to the tab title. Now, you will only get the defaults when you make new tabs/windows and your manual changes will persist and not reflect the variables that endeavor to provide status each time the command line prompt is regenerated.