How do I rename an app in MacOS properly?
Renaming the .app package in Finder only changes the name there, it doesn't change the name shown in the menu. To do so edit YOUR.app/Contents/Resources/XY.lproj/InfoPlist.strings (with XY being the language you are using) and change CFBundleName there.

For applications without localization files you can also edit YOUR.app/Contents/Info.plist and set a new value for CFBundleName there.