I was going to suggest Burning Desire, but there already appears to be a company named that.
Fire and Friction?
Ignite ?
Fuelogy ?
BriqKing ?
Chick Bricks? (what, that's not your name!?!)
Keep writing down related words until some jump out at you. I wouldn't go for something too quirky, I'd go for a more traditional name for the business you are planning on.
As AC says, it is a traditional type business, so to my mind a more traditional approach would be better. Something as simple as 'John Smith Ltd., Purveyors of Quality Solid Fuels.'
Personal I don't like names that hide behind plays-on-words (and don't get me started on Hairdressers' names!). It is far better to have a 'name' to approach - feels much more trustworthy.
I can't really think of anything as good as the other suggestions however I would advise making it possible to purchase your stock online. You can even have a members area where people 'log' in :)
Write down words that you want to be associated with your business,cut them up and shuffle then around on a table until something jumps out.then Google to find out if someone has the same business name. Don't go too 'quirky' though as it puts some people off. If you name rhymes with anything relevant (Kerry's kindling, Frankie's fuels) that's an idea,as is naming it after the place you live ie Wickham fuels, Lymington logs.