Alaikumassalam wa rahmatullah,
Shazleen is not an Arabic word and not in the Quran. It could come from Shadleen, which in Farsi means "one who has the heart of a king", "golden-hearted".
Shazleen would also refer to the Shazili Sufi group, originally from Morocco. It means "the Shazilis". The word comes from Shazila, a village in Morocco.
You can use the name since it doesn't have a bad meaning. Shazleen may also have other meanings in other languages, the above is what I know.
Sufia/Sophia/Sofia means "wisdom" in ancient Greek. In Arabic Sufiyya means "female Sufi", a female follower of Sufism, or a woman who is ascetic and lives for the sake of Allah. A similar name is Safiyya, which means "pure", "chosen". These are the only close Arabic words. Their meaning is not bad therefore you can use them. Sufiyya is not mentioned in the Quran directly or indirectly. Safiyya is an indirect Quranic name.
Shanzay is not an Arabic or Quranic name. It seems to be from Farsi or Urdu origins. The Sha part means king, royalty. I am not sure about the nzay part. Some sites say the name means "princess", and this is probably since the name has the Sha in it. Since the meaning isn't bad you can use it.