A very good question, tho i do not have a non-surname..I have 2 born out of wedlock..a mother and daughter, the mother, spanish (born about the same time as yours) took her mother's surname, father unknown. the daughter, father known, at first went by mothers previous marriage name, then later took on father's name. i have not been able, so far, to find a precedent for this.
what i do know is that pomo natives in my family took on their what i call 'master's' name, the spanish and americans whom they labored for..
or, the mother's maiden name was prob? used.