How can I find out the make of my old kitchen cabinets?

There are so many cabinet makers, and some aren't even around any more. I doubt if you could find out. Many of the cabinetry use the same patterns too.

You could ask around your neighborhood and see if anyone know who made the cabinets. I had this issue and my neighbor knew who installed them.

Are they wood or metal? If metal, you have a better chance of finding the manufacturer. If you have one cabinet away from the others, maybe it can be taken down to see if there is a maker's mark on the back.

check on the back of the cabinets there might be a sticker or something written on the wood

Many custom cabinet makers will place something inside a cabinet or two, but back in the day it was not "a thing" like it is today. Still look for a manufacturer on the inside of a cabinet door or back of cabinet. If you think they are original to the property and really want to dig, head down to city hall and see if they have the original permits on file for your piece of property and possibly even the blueprints. Many times the subcontractor list is contained in those documents - and get a great history lesson to boot!