Basically, there are only two different ways to hold a hook. One way is underhanded-the way most people hold and ink pen. I say “most” because I’ve seen people who have their own flair for welding a writing utensil. As you can see, in the photo below (and please excuse the notebook background, but I wanted to get the photo fast to demonstrate the underhanded method).

Then, there’s the overhand method. This is very similar to how a young child will hold an eating utensil. See the photo below.

In both of these photos, you’ll notice there is no flattened thumb hold on this particular hook. But, the placement of my thumb is where the flattened thumb hold would be if it had one. You will also notice that the hook is held facing toward myself. This is the one rule the I do insist that my student use. The purpose being that this grasp will eliminate a lot of unnecessary movement of the wrist; thus, lowering the chance of developing a soreness in the wrist or even carpel tunnel syndrome.
In the 45+ years that I’ve been crocheting, I’ve held my hooks in multiple variations of the two grasp above. I’ve found that with holding my crochet hooks, with the hook held forward, I only need to use a small movement to do a yarn over, to turn the hook downward so the loop can be easily drawn back through the stitch it was inserted in and to complete every stitch thus known to the crochet world.
That being said, I’ll now tell you the situation where I change my grasp. Thus being when working with hooks size Q and up. Sometimes, I also will do the overhand method, using a size P, if my wrists are feeling tired from crocheting for long periods of time. Thank goodness there are a number of ergonomic crochet aids to help with painful wrists, and more continue to be designed everyday. If you have difficulty crocheting for more than 30 minutes or so, I highly recommend that you check into some of these item. I have a few of them and absolutely love them. Another suggestion might be to purchase some oven-safe clay and wrap it around one of your hooks (to test) and then give the hook a little squeeze; as you plan to hold it to crochet. This is give you your own ergonomic hooks, that you’ve designed, specifically for your own hands.
I hope you’ll give these methods of holding your hook a try. Even mixing them all (if you’re an accomplished crocheter) so that you can give your wrist tendons and ligaments a change of pace; thus, reducing the chance of possible severe injury to your wrists.