In this particular case, I’d lean towards hyphenating. Something about [name_f]Quinn[/name_f] Joy-Nicole [name_m]Smith[/name_m] (example surname) seems less choppy to me than [name_f]Quinn[/name_f] [name_f]Joy[/name_f] [name_f]Nicole[/name_f] [name_m]Smith[/name_m].
However, I do think the variety of sounds makes [name_f]Quinn[/name_f] [name_f]Joy[/name_f] work even without a second middle. They’re both one syllable, true, but they’re very different in terms of sound, letters used, and amount of letters, which adds additional flow compared to [name_f]Quinn[/name_f] [name_f]Claire[/name_f] or [name_f]Jane[/name_f] [name_f]Joy[/name_f].