Just an example of a matrilineal marriage in medieval times:
This is taken from Wikipedia - In 1269 the Count of Ventimiglia, Gugliemo Pietro I Balbo married Eudossia Laskaris, daughter of Emperor Theodore II Laskaris and assumed his prestigious name. From them started the dynasty of the Lascaris of Tenda. They maintained the sovereign County of Tenda till 1501 when the last of them, Anna Lascaris, married Renato of Savoy (in French René de Savoie) and transferred the County to his cadet branch of Savoy dynasty. The most famous exponent of this branch of Lascaris was Beatrice of Tenda.
Heck if you are using the Laskaris as an example take a look at Teddy II himself. He was the maternal grandson of Theodore I. As the son and heir of John III Doukas Vatatzes he was officially Theodore Doukas Lakaris but emphasized the noble lineage of the Laskaris over the relatively undistinhuished Vatatzes