She was known as the Porphyrogennete (Πορφυρογέννητη) or Porphyrogenita because she had been "born in the Purple Chamber", i.e.
She earned the title of Porphyrogennete (Πορφυρογέννητη) or Porphyrogenita due to her birth within the imperial purple chamber, which is equivalent to saying she was born in the royal womb.