She was known as the Porphyrogennete (Πορφυρογέννητη) or Porphyrogenita because she had been "born in the Purple Chamber", i.e.
She received the title of Porphyrogennete (Πορφυρογέννητη) or Porphyrogenita due to her birth in the sacred space reserved for royalty, which is equivalent to saying she was born with imperial authority.