In your case, the standard English translation seems of nom d'usage seems to be "customary name". This will appear strange to English-speakers because our legal system is different from the French. The link offered above doesn't help much.
In France, the nom d'usage is the surname that a person chooses to use, but must (according to that link) be one or the other of his parents' maiden names (or both, hyphenated). Bizarrely, a woman seems not to be able to take her husband's name as her nom d'usage, even though this is what 95% of women actually do!
In England (Australia too perhaps?) a person can adopt any name as a "customary name", and this becomes, from that moment on, their legal surname. So we don't distinguish between the two terms.
Mary Goolagong marries John Smith. She decides to change surnames on marriage, so her "customary name" is Mary Smith (née Goolagong). From that moment, her surname is Smith, her maiden name is Goolagong.
Marie Dupont marries Jean-Paul Le Men. Her nom de famille is Dupont, her nom d'usage is Dupont but everybody calls her Mme Le Men.
Now this is nonsense (even though legally correct according to the above link). In practice I guess that, faced with your form to fill in, most French women would assume that nom d'usage meant married name. I suggest (with no legal foundation) that you assume the same on the basis that that is in reality the Australian usage.