I'm really not clear what her family name really is. Other places call her Celestine Call. I would guess that her real name is most likely to be Celestine Cole, which would I think be transliterated as Коол.
If her name really was Cool (possible, but would be a very unusual surname), then the correct transliteration would be Кул.
A book on Paul Robeson (available in Google Books) calls her Cole. I can't remember what the Starr's book 'Red and Hot' calls her but a web reference to the book says Celestina Cole.
She seems to have been quite unknown outside Russia. Both may be assuming this spelling as I am, but it does seem the most likely. Cole is quite a common name, Call and Coll exist but Cool seems very rare to non-existent as a name of British origin.
I imagine it depends on whether it's a true transliteration of the sound or just done from the spelling.
As the translation was made more then 10 years ago, now I can assume that the proper spelling should most probably be "Cole". "Целестина Коол" seems to be an archaic transcription; the more modern Russian version, I think, should look like "Селестин Коул".
We may never know for sure but it's a good assumption. I wonder why she was in the USSR (classical singing training?) and what happened to her?
Alexey Batashev writes about this Black singer in his "Soviet Jazz" (Moscow, 1972, p. 46):
"Celestine Cole - a young American, that was invited to [the USSR] by her relative, a worker Robert Robinson, who has just acquired Soviet citizenship. Robinson worked on one of Moscow factories and was elected a Deputy of the Moscow Soviet. From 1934 until 1937 Celestine Cole studied singing in Moscow and gave performances with various variety collectives in lots of the cities of our country"
And, just to add, the full name of Varlamov's orchestra at the time of this recording was "Jazz of the Central Red Army House"