Clanging refers specifically to behavior that is situationally inappropriate. While a poet rhyming is not evidence of mental illness, disorganized speech that impedes the patient's ability to communicate is a disorder in itself, often seen in schizophrenia.
^Formal thought disorder in schizophrenia: a factor analytic study. Peralta V, Cuesta MJ, de Leon J. Compr Psychiatry. 1992 Mar-Apr;33(2):105-10.
^Schizophrenia and the structure of language: the linguist's view. Covington MA, He C, Brown C, Naçi L, McClain JT, Fjordbak BS, Semple J, Brown J. Schizophr Res. 2005 Sep 1;77(1):85-98. Epub 2005 Apr 2.