Like others I understand how you feel guilty.
However, even if you'd given your name... it might not have stopped her before they arrested her.
One of my sister's best friends (a teacher at that time) saw a mother hitting her own son in the school parking lot. She looked up and saw the teacher and said, "If you call the cops, I'll just beat him harder when I get home."
You at least told the cops... but there's no guarantee she wouldn't have hurt her own daughter harder just to punish her for it.
And it sounds like you're thinking, "Maybe if i'd pushed harder, the girl wouldn't have been sexually abused... maybe the abuse would have stopped at just her being hit." but ... unless you know them personally, know what happened behind closed doors... it may have already been happinging.
but ... just think... the girl is away from her now... and you helped protect her