I'm just guessing that maybe you are referring to a male name Kaz, or Kazu, which is normally an abbreviated version (nickname) of longer names such as Kazuo, Kazuhiro, Kazuhiko, Kazutoshi, etc., etc., there are many male names that start with kazu-.
Definition of Quatrain. A quatrain is a verse with four lines, or even a full poem containing four lines, having an independent and separate theme. Often one line consists of alternating rhyme, existing in a variety of forms.
Thus, the definition of quatrain most certainly existed before the word that we now use. Forms of Quatrain. Heroic Stanza or Elegiac Stanza: This type of quatrain is written in iambic pentameter and has the rhyme scheme of either ABAB or AABB. Rubaâi: The rubaâi, or rubaiyat in plural form, is a Persian quatrain. The rhyme scheme and meter that are used in the four lines of a rubaâi quatrain are very specific.