First of all, check the tuning of your drum, including the “tuning” of your snare wires.
Secondly, your drum *should* be able to produce a few different, usable sounds. If you hit it dead center, it should be snappy and dry. If you hit it just off center, it should add some body to the sound. If you hit it just outside of that, maybe 1.5”-2” off center, it should give you an “open” sound. I play around with these sounds all the time. Like, if I want a tighter sound for the verse, but then want to open up the sound to be bigger for the chorus, I’ll adjust where I hit the drum, accordingly—not unlike playing the hi hats with the tip of the stick, the shoulder of the stick, or having them slightly open for different sounds.
After playing for a while, if you want to pay attention to such things, you’ll get used to playing the drum in the different areas without looking, just like you can learn to play a rimshot without looking. It’s about the feel of the drum and response of the sound.
But, yeah, first thing’s first: check your tuning.