If you are trying to have the same enumerated name in the same ASN.1 module, this is not permitted. If you have two separate ASN.1 modules which are different versions of the same specification, each of which has some types with the same names, some ASN.1 compilers will automatically disambiguate the conflicting names for you.
Having the same type name twice in the same ASN.1 module is not permitted, but having two versions of a module (with some differences between them) is permitted. Backward compatibility between those two modules needs the guidance of an ASN.1 expert in order to avoid interoperability problems.
An excellent place to try your ASN.1 specifications to see what it valid is the free online compiler and runtime at http://asn1-playground.oss.com.