When a peeress (ie a duchess, marchioness, countess, viscountess or baroness) obtains a divorce, the general rule is that she places her forename before her title, for example, Mary, Duchess of Hampshire. This is purely a practical measure to avoid confusion should the peer in question marry again.
In the event of a divorced peer remaining unmarried there is no reason why his former wife should not continue to use her title without the qualification of her forename. A case in point is the Countess of Lichfield.
If Miss Jane Debrett marries the Hon Michael Hill she becomes the Hon Mrs Michael Hill. On divorce she should be Mrs Jane Hill (since the courtesy title belongs to her husband).
When the Hon Caroline Woodhouse (daughter of a peer) marries Mr Debrett she becomes the Hon Mrs Debrett rather than the Hon Mrs John Debrett. Unless the woman he remarries is also a peer’s daughter, she can continue being named the Hon Mrs (no first name) Debrett, which differentiates her from her successor. However, it is more common now to use the Hon Mrs Caroline Debrett, with the first name reinserted.
For further details see Forms of Address/Titles or click on the appropriate link below: