Most of the modern-day names and terms associated with Hephaestus are related to his Roman counterpart--Vulcan. Here are several examples:
Vulcan Equipment--a company which specializes in restaurant items such as ranges and other "heating" kitchen elements. Because of the connection to fire and heat, the company's name works well for the god.
Vulcan Materials--a company which offers stone and construction materials; again, this connects well to the god because of his forge and other heavy manual labor tasks.
Volcano--this term does come from Roman mythology, obviously because of the fire and heat association.
We can find many companies that take their names from ancient mythology. Trojan, Argus, Amazon and Ajax are just a few. As far as the god Hephaestus is concerned there are a few major companies named for him and some named for the Roman name of the same god, Vulcan. Hephaestus Consulting Inc. is located in Pennsylvania. It is named after the lame god Hephaestus, who was the god of fire. He is also widely recognized as the patron deity of the metal workers. Being from the Steel City of Pittsburgh, I am very familiar with Hephaestus and his place in the steelworker’s culture. Hephaestus Consulting is a corporation involved in the reheating and heat treating furnace business.
There is also the famous Hephaestus Holdings, Inc. ("HHI”). This company is a subsidiary of Impact Forge Group, Inc. and Kyklos Bearing International, Inc. (“KBI”) subsidiaries. These companies combine to create the largest independent manufacturer of forged parts and a leading manufacturer of wheel bearings for the North American automotive industry.
Hephaestus is not only the fire god, but he is also a great maker of things or a craftsman. So, any store or company that deals in fire or crafts may want to use the name in some form. A little search will offer a few companies that actually follow along this path in their name. Here are a few:
1. Hephaestus Palm Spring is a jewelry company. Presumable they make excellent crafts in terms of Jewelry.
2. There is also a company called Hephaestus Fashion Creation. They make clothing.
3. There is another company called, Hephaestus Consulting. They deal with heating issues. I am sure, because they are referring to the god of fire.
I will link the last one to this post.
There is a park and museum, named Vulcan. You might know that Vulcan is Hephaestus's Roman name. The park and museum has a 56 foot tall statue of Vulcan! This park is located in Alabama.