I agree with the others that any form of name tag would be wrong. The longstanding policy of “name is the name only” definitely applies here. If these roads aren’t actually named “Causeway (Heavy Vehicle)”, etc. (which seems very likely), then these ways shouldn’t have a name at all. Any access restrictions should be tagged using the relevant access tags and then data consumers can decide how they want to handle each case.

On a side note, there’s nothing wrong with using language suffixes on any name-related tag if that’s approriate. I’m not sure where you saw that this is not allowed. It’s only logical that int_name, nat_name, alt_name, old_name, etc. could potentially exist in multiple languages.