The form of Dionysos worshipped by Phryne was Dionysos Isodaites. “He Who Divides the Sacrifice Equally”

Phryne was accused of asebia because she held a komos in the Lykeion. This is what Euthias, who prosecuted her, said: I have now proven that Phryne is impious because she has participated in scandalous revelry, because she has introduced a new God, and because she has assembled unlawful thiasoi of both men and women.
— Works of the Attic Orators 2.320

Isodaites. Mentioned by Hypereides in his oration for Phryne. Some foreign daimon, in whose honor women of the lower classes, and particularly the ones that did not excel in virtue, used to hold teletai.
— Harpokration, Lexicon s.v. Isodaites

As for his passage and distribution into waves and water, and earth, and stars, and nascent plants and animals, they hint at the actual change undergone as a rending and dismemberment. In addition to Dionysos he is called Zagreus or Nyktelios or Isodaites. Deaths too and vanishings do they construct, passages out of life and new births, all riddles and tales to match the changes mentioned. So they sing to Dionysos dithyrambic strains, charged with sufferings and a change wherein are wanderings and dismemberment.
— Plutarch, On the E at Delphi 9

I think this really goes to show the egalitarian nature of Dionysos’ religion. He divides the sacrifice equally. He brings us all together under His banner. No matter who you are, where you’re from, who you love, you’re always more than welcome to don a stephanos, daub your face with titanos, and rave with Dionysos’ people. Io Dionysos Isodaites! May we all enjoy a portion of the sacrifice!