Given this sentence:
El chico le da el reloj a la chica. The boy gives the watch to the girl.
Can I rephrase it into this?
El chico le da el reloj.
Given this sentence:
El chico le da el reloj a la chica. The boy gives the watch to the girl.
Can I rephrase it into this?
El chico le da el reloj.
Yes, that's fine, as long as the context makes clear who's receiving the watch, in other words, as long as we know whom the "le" is referring to. The equivalent sentence in English would be
The boy gives the watch to her/him.
Or:
The boy gives him/her the watch.
Yes you can but it would be the same in English.
In English you could say The boy gives the watch to the girl or you could say The boy gives the watch but in the second case to whom would be implicit or known from context.
In Spanish would be the same. El chico le da el reloj a la chica has a full meaning while in El chico le da el reloj it is unknown to whom unless it is implicit in the context.
So if you want to keep the same exact meaning you can not rephrase one into the other but both sentences are correct and if the contexts clarifies the object of the gift then yes, you can use either one.