If what you need if to change the shipping title of carrier-calculated shipping rates, this is not possible.
There are many threads talking about this, for instance:
Is this what you are trying?
Have you try going to Settings > Shipping and Delivery > Then in the shipping section "Manage Rates" > there in the "economy shipping" click on the 3 dots and click Edit Rate > Edit rate name
Nobody ever has this problem? Is this because most users use generated rates?
I like to put the estimated of days shipping takes in the shipping rate name, something like 'economy (10-20 days)' but if things change because of for instance pandemics then I have to go through 100 or more entries to change the name...
Can i request collaborator access to your store to take a look?
if show please share store url here or by PM