Cheesecake in rectangular pan
You can of course, try this.

The largest challenge you will face is that cheesecakes are notoriously difficult to release from the pan, and they are not very strong.  The traditional crumb crust is also not very strong, so it doesn't provide much support or structural integrity to the slice.

This is why spring form pans are normally used for cheesecakes:  they let you leave the cheesecake on its base plate, and just remove the ring.  The crust sits on the base plate until service.

If you want to try it in another pan, to facilitate getting it out, I suggest that you:


Consider using aluminum foil instead of parchment, as it is easier to shape.  Make a sling for the cheesecake, so that the foil comes up the edge of the pan.   You will want to do this in both directions. 

The sling will be used after baking to lift the cheesecake out of the pan.  You should then be able to carefully peel the foil back from the edges, and slice it.  (Many brownie recipes recommend this technique.)
Consider a sturdier crust than a crumb crust, perhaps a full shortbread, that will survive the lifting from the pan, and be strong enough to support the pieces when you cut them.
Changing the shape of the pan may change the surface area of the cheesecake, and thus its depth, which will affect the cooking time.  You want to choose a new pan that is as close in area to the pan anticipated in your recipe as possible, so that the baking time and temperature do not have to be adjusted too much.  Getting the perfect balance of time, temperature, and thickness of the custard is a tricky matter.

If your original recipe calls for a 9" spring form pan (which is fairly typical of cheesecakes), that is approximately 64" square inches.  So you would choose an 8x8" square pan to have approximately the same area.

A complication is that spring form pans tend to be taller than square cake pans, and cheesecake recipes often take advantage of this fact.  If all of your filling will not fit (with some reasonable room for a tiny amount of expansion (cheesecake should not really expand when cooked), you are going to have to adjust the baking time and possibly the temperature.

Your cheesecake should be done when it jiggles slightly at the center, and has an internal temperature measured in the center of approximately 180-185 F.  You will need an instant read thermometer to measure this.

If you are changing the depth or the area, you will definitely want to monitor your cake closely for when it is done. 




Another approach would be to make individual cheesecakes or tartlets in a tartlet mold.


You should easily be able to google many suitable recipes.