I've researched this question on and off since it was posted, and I can find no source indicating that "Pon Farr" was named after the Pons.
That being said, I looked closely at the authorship of the script for "Amok Time". While the final product is attributed to Theodore Sturgeon, the drafts went through several hands before his. One of the people who worked on it was Kellam de Forest (not to be confused with DeForest Kelley). Kellam de Forest was hired by Gene Roddenberry to fact-check scientific, cultural, and historical facts in TOS scripts, as early as "The Cage".
For example, de Forest introduced the idea of a silicon-based life form in "The Devil in the Dark". He also made sure the Greek gods in "Who Mourns for Adonais?" had Greek names (and not Latin ones, which apparently were in the original script). I have to assume that de Forest did not consult on "Spock's Brain".
Regarding "Amok Time", the story idea was originally written down by Roddenberry, Gene L. Coon, and D.C Fontana, and then passed to Peter Sloman and Joan Pierce, de Forest's research assistants, presumably to consult on the plausibility of Spock's condition. This was prior to Sturgeon receiving and finalizing the script. (Sturgeon's main contribution seems to be taking the Enterprise to Vulcan. Originally, T'Pau was to have come aboard the Enterprise and she and Spock would have been the only Vulcans in the episode. Sturgeon introduced many aspects of the Vulcan language while doing this.) The development of the script is described here.
It is plausible that de Forest and his assistants had named Pon Farr after the part of the brain that is responsible for the mating urge — the Pons — as part of their fact-checking assignment.
However, there is no direct confirmation of this.