Is there a way to tell what frequency an unmarked antenna is designed for?

No, you can't really tell by looking at it, at least when all the details are covered with a skin so you have no idea what might be inside. If those markings are in mm (it would be helpful to say), then it's probably 910 MHz, but again, there is no way to know without measuring it.

You don't even know if this is a self-contained antenna or one intended for use with a ground plane. That makes a factor of two difference in size right there. Then these kinds of fully assembled "rubber duck" antennas have reactive components inside, so you really can't guess much what frequency it will resonate at without measuring.