faucet brand

We have a garden tub with fixtures original to the house (built 1989-90). We've never used the tub; however, recently we checked the faucet to ensure that everything works as it should. First, although both the hot and cold do work, the cold water only trickles - even when fully open...

I need to repair this faucet, but I do not know how to disassemble the handle. I would think that the Top cap screws or snaps off. There are no set screws.