When can I use my husband's last name socially?

I did not change my name after getting married, and am considering adding my husband's last name after my last name now that we have a baby, mainly in scenarios where the context of shared last name with my baby would be helpful. (Meeting other parents, etc.) If I don't change it legally, in what scenarios would I need to give only my "legal" last name, and when can I use the additional last name socially?

For example, is a school required to have only my legal name on file?