I know a man who has an anvil I'm not familiar with. 

It is a farriers anvil with a swelled horn that is up swept .

I am not finding any information on this brand is anyone familiar with an anvil marked JK?

It appears to be cast and the logo is positive

That may be Jim Keith, who was a farrier in Indiana from 1972 until his death in 2020. I know he had a line of hand tools, and it's possible he had anvils as well.

Jim Keith did sell anvils, there is an old 2008 thread about them but since his passing the link (Blacksmith and Farrier tools) no longer works.