It is highly likely that the Wicked Edge name is trademarked, so you would need a lawyer and a contract with Clay to govern the use of it. It is likely possible, but not financially worth the cost to make it happen.
Usually, those owning the rights to a product name are rather particular how it is used because it can be used easily in a manner that the owner didn’t intend, then the owner of the trademark runs into a problem with reputation.
I could see here that if you put that on your card, the risk Clay is taking is that if you sharpen with the Wicked Edge as part of your business theme, then if you have a deficiency in your ability to sharpen a knife to the customer’s preference, or whatever, then that customer may attribute that problem to the Wicked Edge and you, or just the Wicked Edge. I would imagine that you would want your business sharpening to stand alone, without having to use the Wicked Edge name to stand it up.
Of course, if someone asks what you sharpened with and you tell them a Wicked Edge, that will happen and usually would, but then it is seen as the tool and Wicked Edge being affiliated legally with your business.
As Josh stated, Clay would determine.