Personally, I prefer a symmetrical way of holding sticks (so-called Match Grip) and nowadays the vast majority of drummers play in this way.
However, there is another popular drumsticks grip, called Traditional Grip, used mainly by jazz drummers, but not only.
Traditional Grip was born even before the appearance of the first drum sets, in marching orchestras, in which drummers played (and still play today), with a drum (snare drum or other) suspended in front of them.
Often, such a drum was placed at an angle (above the left shoulder of the drummer) so that it would be more convenient to hold it while walking in the orchestra.
Because it is difficult to stroke with the normal technique when the snare edge is more or less on the shoulder line, it was invented to grasp the stick with your left hand in a different way. And this is how Traditional Grip was created.
How to hold a stick using the Traditional method?
The stick rests between the thumb and the fingers joined together: the second and third finger, and the fourth and fifth.
You can first "make a handgun" (thumb up, second and third finger straightened and joined, and the fourth and fifth bent), then place the stick between the thumb and the groups of fingers described. Then slightly bend your thumb, embracing the stick from the side and the second and third fingers, embracing the stick from the front.
In this way the stick is held in the "snare" hand, ie your left, if you are a right-handed drummer.
In this technique of holding both the wrist and fingers work, which set the stick in motion.
The handle of the stick itself with your thumb gives it energy - you can hit it by embracing the stick only with your thumb.
Another "driving" muscles group are the second and third fingers - by bending and straightening the stick is set in motion.
This way of holding the stick does not provide as much impact force as a normal Match Grip, but it engages the fingers more strongly, which ensures higher speed, and also makes the snare drum hit softer than when you hold your left hand like that as well as the right one (Match Grip).
You can try another method based on Traditional Grip, i.e. place the stick between your thumb, forefinger and the other three fingers (i.e. the stick rests on three, not two fingers).
It gives yet another impression of playing (fingers are not so unnaturally separated from each other).
In this way, one of my favorite drummers, Sean Rickman, is holding the stick. Check out this guy if you don't know him because he plays very well.