When making a purchase, you can do a different signature each time. You can doodle, draw a straight line, write your name, mix it up, whatever. The only value of the signature is that if you don't recall making a purchase, they can send it to you and it can help trigger your memory or make you trust whether or not the purchase was actually you. So it's not for them to use in the verification process. It's for us to help trigger our memories.
When I was living in the UK (which wisely uses a more sensible PIN system instead of signatures) I was shocked the first time someone asked to see the back of my card. I don't think it's ever happened to me in the US. Culturally we've collectively decided to ignore the whole "signature verification" thing, but when using your card abroad you sometimes are reminded that it's supposed to happen in theory.
The fact that you can put any doodle you want in there is because the vendors have decided it's cheaper to absorb the fraud than to check the signatures.
So clearly, that's not how the signature is actually used. What matters is how it's actually used, which is to help prevent good faith actors from accidentally reporting purchases as fraudulent. That's a valid use, but noteworthy.