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.
A couplet is a pair of lines of metre in poetry. Couplets usually comprise two lines that rhyme and have the same metre. A couplet may be formal (closed) or run-on (open).