My sister and her DP are not married, but living together. She has two boys from previous relationships and together they also have a 9 month old baby girl.

Her first son has her surname (dad not involved at all), her second son has hyphenated names (her surname and her first husband's surname) and the newest addition carries her DP's surname only.

So I'm sure they can either name, so whatever sits best with you.

love
sushee