Heil=Comfortmaker=Tempstar=ArcoAir (made by ICP which is owned by Carrier) ICP=intercity products or International Comfort Products
Carrier also owns the rights to Clare
Lennox (now owns Ducane)
Amana=Goodman (within the past couple of years)
Older Goodman used the Janitrol name
There really are only a handful of parent companies for furnaces these days, but a ton of name brands. People tend to buy brands they know and trust. It really has nothing to do with the company that actually manufactures it. Installation is the most important.