If you live outside Dennmark and have changed your name and wish to inform the Danish authorities of this change, you have to apply for a new passport.
For further information on how to apply for a new passport and what documents to bring please see the section Passports.
Denmark follows the domicile principle, i.e. you must follow the regulations for changing your name in the country where you are domiciled.
Taking your husband's name without the use of your former surname as a middle name:
Danish women domiciled in the UK at the time of marriage, no matter whether this took place in Denmark or in the UK, can apply for a new passport in their new name by simply producing the Marriage Certificate.
All other changes of name including using your former surname as a middle name, husbands taking their wifes' surname, require a Deed Poll (see below).
If you wish to double-barrel two surnames the easiest way to do this is for the husband to change his surname by Deed Poll before the wedding to the double barrelled name .Then after the wedding the wife can use her Marriage Certificate to apply for a new passport in the new name.
To change your name by Deed Poll please visit the website of the UK Deed Poll Service: http://www.deedpoll.org.uk
All changes of name obtained in the UK by "Deed Poll" must be legalised by the Foreign and Commonwealth Office's Legalisation Department before you can apply for a new passport.