Is it possible to have 6 sessions each of 15 minutes instead of a one hour session?

A session of 15 minutes is not long enough to achieve a good result. A session of at least one hour is always advised, and in fact is the minimum possible with an authentic CoolSculpting machine. I can't imagine 15 minute sessions achieving any kind of result. I would be concerned about the reputability of this provider and would proceed with caution. It's not possible that they are using a certified CoolSculpting machine.

I have never heard of 15 minute sessions, nor is it recommended. It takes the full cycle time for fat to reach the proprietary temperature in order to actually induce the death of the fat cell, otherwise you will not achieve the 20-30% reduction seen in all clinical trials and scientific papers. It can be done, but results will not be the same.

Zeltiq is the company that owns the CoolSculpting brand. Zeltiq sells physicians the machine, applicators, and consumables in order for practices to deliver treatments to their patients. The machine will not function without using a cycle on a preloaded card, the cycles are a minimum of one hour each. Because of this simple fact I can tell you with absolute certainty that the practice that you have spoken with is not offering an authentic CoolSculpting treatment.

You are probably not getting cool sculpting.  Those treatments are preset to 1 hour each. You cannot break up the treatments.  

First of all--be sure you are being treated with a Zeltiq Coolsculpting machine. In order for this procedure to work properly it takes one hour with the suction applicators and 2 hours with the Coolsmooth applicator. Anything less will not be effective, and is not an option for proper treatment.