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'Wash' does not mean 'face'. It is a particle of similitude added to nouns (Steingass Persian Engl. dict. p.1468). So the meaning given in this database for Mahvash is correct (except that it includes the word 'possibly'). The intended meaning is, as you indicate: 'one whose face is beautiful like the full moon'.
Mah, 'moon', has 2 forms: with long or short vowel. It is very strange that you think 'meh' MUST be wrong because it means something else in another language... Where is the logic in that?