For British and Irish citizens who are travelling on flights to/from the United Kingdom, to/from the Republic of Ireland (Common Travel Area), a valid driving licence with photo is acceptable photo ID. Passengers who are citizens of other countries travelling on these routes must present a valid passport (with visa if applicable) or a National Identity Card issued either by the government of a European Economic Area (EEA) country or Switzerland.
See attached Ts & Cs from Ryanair about ID requirements.
Its always a good idea to carry a passport to a foreign country.
All passengers must present valid photo identification at check-in for all flights. The only acceptable forms of photo-ID on Ryanair flights are:
A valid passport (passport for travel outside the EEA must have six months validity beyond the date of entry).
A valid National Identity Card issued by the government of a European Economic Area (EEA) country. Only the following countries from the EEA issue National Identity Cards which are acceptable for carriage: Austria, Belgium, Bulgaria, Finland, France, Germany, Gibraltar, Greece, Cyprus, Czech Republic, Estonia, Hungary, Italy, Liechtenstein, Lithuania, Luxembourg, Netherlands, Malta, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden (for travel within the Schengen area only) or Switzerland.
For British and Irish citizens who are travelling on flights to/from the United Kingdom to/from the Republic of Ireland (Common Travel Area), a valid driving licence with photo is acceptable photo ID. Passengers who are citizens of other countries travelling on these routes must present a valid passport (with visa if applicable) or a National Identity Card issued by the government of a European Economic Area (EEA) country.
I travelled to Leeds a couple of weeks ago with ryanair on my driving licence. So they do accept that as a form of ID.
There could be a problem there, with the maiden name and surname being wrong. If you can sort out the name change on the licence you shouldn't have a problem.