Don't claim to know the full in's and out's, but supposedly
Prestwick wasn't used in the early days for the ACC because the Prestwick Oceanic Area Control Centre (POACC) had already nabbed it.
NATS have now more or less dropped the word
Prestwick in this context and now simply refer in print to the "Oceanic Area Control Centre" located at Prestwick. (Despite the brass plaque in the corridor outside the old Ocean ops room and beside the entrance to the new still bearing the 'P' word).
A precident has already been set on the other side of the pond where NAVCANADA have seemingly managed to cope very well with an ACC which deals with both oceanic and domestic traffic from within the same ops room, while using the same ident:
Gander. Can't see the problem with a single ident, after all, if the Canucks can cope, I'm sure we'll do likewise. With "Shanwick" being used alongside "Prestwick", unlike the situation with Gander, there'll be absolutely no chance of confusion between domestic and ocean.
(BTW, the only time a Shanwick ATCO is likely to I-D themselves as being "Prestwick" is to Shanwick Radio Operators at "Ballygirreen", otherwise you'd get a situation of "Shanwick", "
Shanwick", "No, this is Shanwick" "
No, I'm Shanwick, you called me" "Negative, you called ..."
)