A close friend of mine was in the same situation as you, she had 2 kids though. She just used her new husband's name as her kids surname. The were still legally known as the father's surname as far as documentation, bank accounts etc were concerned. She enrolled them in school as their birth surname but they were referred to as new husband's surname on the roll.

These kids are 23 and 21 now and both have changed their surnames legally by d-pol.