Sonya Name Meaning. The meaning of Sonya is “Wisdom-dim. of Sophia”. Keep in mind that many names may have different meanings in other countries and languages, so be careful that the name that you choose doesn’t mean something bad or unpleasant.onya Name Meaning. The meaning of Sonya is “Wisdom-dim. of Sophia”. Keep in mind that many names may have different meanings in other countries and languages, so be careful that the name that you choose doesn’t mean something bad or unpleasant.