I think rare letters add a beautiful, exotic quality to names, and I immensely prefer a name when it has one (or more!).
My answers:
Q:
Enrique,
Monique,
Quiana,
Quinn,
Quinton,
Raquel,
SequoiaX:
Ajax,
Asterix,
Alexandra,
Bellatrix,
Hendrix,
Jaxxon,
Lexi,
Max,
Phoenix,
Polyxena,
Roxy,
Trixie,
Xanthe,
Xavier,
Xenon,
Xerxes, Xiamora
Z:
Azure,
Jezebel,
Zaccai, Zada,
Zaire,
Zakaria,
Zendaya, Zenith,
Zenobia,
Zephyr,
Zinnia,
Zoey