Surnames were not used in Britain until the 11th Century and there are records of Matthews back to about 1260. There seems to be some dispute about whether the name is properly spelt with 1 or 2 Ts, but there is some support for the idea that 2-T Matthews comes from Wales in the family motto:
Y FFYNNO DUW Y FYDD
(What God willeth shall be.)
(What God willeth shall be.)