The later BMT standard cars (not sure of the numbers)
2500-2899 and 4000-4049, 2500 series was ACF, the rest Pressed Steel.
had larger roll signs in the windows (in place of the ones in the door pockets). On those, there were indications something like (picture the middle line larger type than the top and bottom lines:
VIA BRIDGE THRU
N A S S A U L O O P
VIA TUNNEL TO B'KLYN
Just substitute BRIDGE<-->TUNNEL etc. for the other direction.
However, I don't recall these being used on the Nassau Loop trains on a regular basis.
They, and the older standards had a "Nassau St" indication, and I do recall seeing that used often.
The large sign NASSAU LOOP designations were used all the time on two services, the West End Short Line, which ran north through the loop, and the Culver Express, which ran south, both during rush hours.
In the early 1960s, the AM Brighton specials (Standards) were usually signed (the two sets on the Standard cars):
Express
Nassau St
and
Express
Chambers St
My memory is a little different, possibly because I recall when the Brighton Specials ran SOUTH through the loop. It was EXPRESS / BROAD STREET and EXPRESS / NASSAU STREET. Whether the one sign said BROAD or CHAMBERS might have been indication of whether the train was running north or south through the loop.
Of course, in those days, the trains deadheaded back to Brooklyn via the Manhattan bridge without passengers.
Practice varied. On West Ends and Culvers you could ride the whole thing. On the others, the schedule shifted.