Interesting comments aside, the answer to your question as to how to mark the relationship between the pun and the punned seems to be clearly "pun on". Here is an ngram analysis comparing the usage of "pun of", "pun on" and "pun based on" and "pun on" is the clearly dominant phraseology.
µDP is a pun on ...
It is required to do so by law or by the regulations of any relevant
stock exchange or other regulatory authority [the rules and regulations
of which he or it is subject to].
"To" is required.
In the bracketed relative clause "which" refers to "regulations of any relevant stock exchange or other regulatory authority".
Your question incorrectly presupposes two things:
A preposition such as of takes as complement only a noun phrase (a phrase headed by a noun).
Although a preposition typically takes a noun phrase, it doesn't always do. Here are some counterexamples:
a. get out of here
b. of late
c. in spite of me not having studied much for the exam