Change the name!
“Local” is a terrible name for a web software product for these reasons:
It’s confusing to talk with support about “My local site (could mean a wide range of things)” vs “My
Local(the program) site”
It’s impossible to google for general help “Local site not working” “Can’t upload local site” is useless in terms of specificity. No way to tell google you’re referring to Local
The word “local” seems to interfere with some Apple Bonjour networking stuff, which natively uses “.local” I’ve heard of and had problems making things work properly for that reason alone, specifically with external services like liveReload and CodeKit not being able to play nicely with “mywebsite.local”
It needs a unique, google-able name. It’s in branding limbo now, being a former Flywheel product that’s still branded to match Flywheel, that now works (sort of) with WP Engine but has no WPE branding. At some point it needs a heavy identity rethink, and that would be the perfect time to change the name!