Book about a girl named Abygail who can travel in time

Question

Does anyone know of a book that satisfies the following properties:

• The book is about a girl named Abygail/Abigail (or possibly another variation of this name).
• The book says that the name "Abygail" is an old witch name.
• The book was published in 2004 or earlier
• The book was written or translated to English (possibly by an English author during the 1990s)
• Abygail can wield magic and travel in time

Answer 1

Playing Beatie Bow by Ruth Park

Worldcat.org abstract:

Disturbed that her mother could welcome back her unfaithful father, Abigail Kirk undergoes a mysterious voyage to nineteenth-century Australia, where her experiences help her to understand the power of love and to accept her father.

The character born Lynette changes her name to Abigail:

'Tell me some witches' names, Mum,' she said.
'Well, there's Samantha, and Tabitha,' Kathy began.
'Oh, I don't want soppy TV names,' said her daughter. 'Some real witches' names. 'They'd have to be old ones,' said Kathy thoughtfully, like Hephzibah, or Susannah, or Petronella, or Abigail. 'That's the one!' cried the girl.
'But it's so plain, so knobbly, so... so awful!' wailed Kathy.
Grandmother smiled. Abigail could see quite easily that Grandmother thought she was plain and knobbly and awful, too. So that settled it.