a question about names

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I am starting the outline of a story and I am curious about characters names. This is set in a fictional world where women are in control and has always been. Its around a 100,000 years from now and its almost inconceivable that men were ever in charge. Women have developed a power long ago to overpower men and gained control. Theres rumor's that men were dominant but its mostly dismissed as impossible

so in this world, should some men be given like female type names to show they are submissive and should women have feminine names since femininity is dominant and and what is thought to be powerful in this setting and men dont see it as being demeaning like in our world

Im just curious about all of this
and what about a male character that feels in between and wants to try to unite the two and not be submissive

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