We had an Indonesian grad student who had only one name and she was insistent that it was her only name and woe betide any professor who complained. The president of Indonesia was (maybe still is) Megawati, but when pressed she made it Megawati Sukarnoputri, pretty clearly a patronymic since Sukarno was her father. Icelanders normally have only one name (there are a few exceptions, mainly for families that had used last names before the law went into effect, although Vladimir Ashkenazy was another). The president was named Vigdis and so referred to by Icelanders, but for foreign consumption she used her patronymic Finnbogadottir. But Icelanders do this as a matter of course, when leaving Iceland, while apparently Indonesians don’t when they leave their country.
That said, nearly every online form I have ever seen will not permit a single name. So even if you call yourself Gastel Nofamilyname you will have to call yourself something.