When can I serve notice

Possession - Section 8 and Section 21

Good afternoon, in would like to serve a tenant notice to leave their property , they have been tenants for approx 12 years on an assured shorthold agreement. I have no dispute with them over rent, and the property has no ongoing repairs. Ithere was no damage deposit paid at any time. Will I have to wait to serve notice on them at the moment, and what time frames am I looking at. I would presume that when I do serve notice, they may stop paying so I don't want to do anything too soon. Also as the couple have married during this time,will I use the ladies new marital name on any document?