Shorter - 2" Overhead or less for a dedicated Surf paddle.
People may say it's a matter of preference but I will wholeheartedly disagree.
When I learned to SUP 4 years ago the mantra was 6" - 8" overhead with Laird and Dave Kalama reaching for the sky and bending their hand over their paddle (more like 10"+++ OH). 9' 6" was a short board. . . .
Then things evolved. Boards got shorter and Connor Baxter introduced a choked down stroke that he used to blow away the competition in the Gorge. I started to use the "Connor Stroke" on paddles range from 6" to 11" overhead to catch waves and found that I substantially increased my wave count (e.g. catch). Then we read about people with head high paddles, COLAS, and watched videos of Zane Schweitzer, Mo Freitas and others tearing it up with short boards and short paddles.
The Connor Stroke permits a racer to have multiple gears. The Choke Down is first gear. When surfing you want first gear all the time because you are launching from a stand still to full speed ASAP just like Connor at the start (see below). So I decided to cut my paddle to head high.
The Short Paddle has been a game changer in the waves. My paddle is head high and I no longer need to choke down because I am already there. The secondary benefit is lower swing weight and maneuverability on the wave (some might claim this as primary). Try doing a Crossbow turn with a paddle thats 10" overhead!
In summary when learning, cruising or racing 6"++ is fine but if you want to push your performance in the waves
a short paddle is like a short board and it is the best way to help maximize your potential.