The change of name would have to be done by transfer deed as per a normal sale/purchase.
If the property is sroted by court order or agreement in the divorce then none will be payable.
If not, whether or not stamp duty is payable depends on the consideration stated in the transfer.
Stamp duty will only be payable if the consideration, ie money changing hands or mortgage liability, is over the stamp duty limit which is currently �175k.
This should help...
http://www.hmrc.gov.uk/so/marriage.htm