With several different navies working in the area, the command structure of each ship does all speak a common language.
And it is most likley english.
English is the common language for air traffic controllers worldwide, with EVERY air traffic controller speaking english only to pilots,so it is also probably the language used by all of the various naval vessels to communicate with each other.
English is the official language for all NATO units, not just a "common language". From the very beginning onwards.
And that because on sea, it's always been the international communication language - though many nations didn't sign the IMO SOLAS (that changed 1974 - though it became really oficially only in 1995).
A personal, anecdotic memory:
in 1972, I was "the voice" (on VHF) of the commanding admiral for a big NATO manoeuvre in the Channel and on the French coast (for one day, the other days only for the German units). I was really glad that I knew from before how (especially) the French and Italians pronounce some English words which are similar in their own language.
It was peculiar funny, however, that the other day - when the Royal Navy admiral was in command - there were a lot of mishearings between the British and US units.