Hello

As far as I know the baby always carry nationality of mother (parent Ius sanguiny) , that's the first option what will be always given in most countries nowadays. unless apply isu soli ( plsce of birth ) but that is very rare nowadays.
Of course baby can have nationality of father too just need to be stated and registered at fathers country embassy in UK . The best would be to contact this(his) embassy after baby is born or even before and ask what you need to register child birth and to get hold of birth certificate . This way baby will automatically get nationality of father and does not need to apply for specific immigration as child of EEA nation.

The baby can also have double nationality (fathers and mothers) but only if country of both parents allow double nationality principle. But with double nationality double duties of citizen arise(like civil service in both countries etc..). That what need to be remembered.