"Measles, mumps, and rubella vaccine" is officially translated into Chinese as, literally, "Measles, mumps, and rubella vaccine". If you add its indication, it will become "Measles, mumps, and rubella vaccine (indicated for the prevention of Measles, mumps, and rubella)". I don't think that is an ideal way of translating this vaccine's name.
Of course, you don't need to add anything to this self-explanatory name. However, in the UK it will often be documented simply as MMR vaccination, or even by the proprietary name M-M-RVAXPRO. But not all vaccines have equivalent vaccines in all countries.