Alaikumassalam wa rahmatullah,
We cannot find any mention of a name like Zuhayz in Sahabi databases. We found one English page that mentions a Sahabi called Ka’b bin Zuhayz, but there is no such Sahabi, it is most likely a misspelling of Ka’b bin Zuhayr.
Therefore you can keep the name Zuhayz with the meaning of Zuhayr, which is “flower”. Misspellings are not big issue as there are many Arabic names that have non-standard spellings or altered spellings and this does not make the name a bad name.