Airbus uses a ridiculous term EOSID - engine out SID - which clearly it cannot be as by definition all a/c from all operators would fly the same procedure if it was a SID. Just another example of their careless use of language.
For your info, my Boeing uses the same term in it's FMS. Nothing to do with Airbus.
EO SID does not mean that all operators would fly the same procedure, just because it is named using the term SID. In fact, it is entirely logical: Engine Out Standard Instrument Departure. Given the FMS uses the term, why not? What else would you call it and does it actually matter what it's called?