Great Phyllis! Indeed, Beata ,is quite popular name in Poland. Every Beata (expecially when young) you may call: Beatka
Phyllis... that is indeed hard one:) The only name - that is at least similar in sound - that comes to my mind is Polish version of Felicia... that is Felicja. It is old stylish Polish name... one can call every Felicja: Fela, Felka:)
But I remembered one more starting with A...
Polish: Agnieszka (Aga, Agniesia, Agusia, Agniecha:)