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.