(1) Daughter of Mar-Vell, sister of Genis-Vell. (2) Quasar died in Annihilation and Annihilus took the quantum bands. Phyla managed to steal them back, so she took up the Quasar mantle. (3) Probably she didn't call herself Captain Marvel because (a) she had the quantum bands, so she was using Quasar's powers; and (b) she had a massive inferiority complex about not being good enough to live up to her father's/brother's name. She didn't feel she was a good enough Quasar, either, but at least the bands kinda made her Quasar regardless.
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(2) Quasar died in Annihilation and Annihilus took the quantum bands. Phyla managed to steal them back, so she took up the Quasar mantle.
(3) Probably she didn't call herself Captain Marvel because (a) she had the quantum bands, so she was using Quasar's powers; and (b) she had a massive inferiority complex about not being good enough to live up to her father's/brother's name. She didn't feel she was a good enough Quasar, either, but at least the bands kinda made her Quasar regardless.