It is always helpful if you mention sources, since I cannot find any that say 'electra' means unmarried. Amber is today quite a popular name for sexy young models, so 'amber' may mean unmarried. Amber is valuable for jewelry which is an asset for young women. Myths are not just made up stories. Myths are stories which someone believes is true.
Some myths seem to be fantastic enough to be made up, but many have a basis in fact.
The problem sometimes is to determine what the facts are. The ancient dramas, such as Electra, were not just for entertainment. They were written to glorify the workings of the divine and to help people understand how the deities worked in the world. The ancient dramatists were trying to bring the ancient myths to life. What they had were ancient epics describing the myths.