Perhaps you meant denatured with methanol? Cooking alcohol is ethanol (the kind of alcohol you drink) and methanol is the poisonous stuff that might be used to denature ethanol.Denatured alcohol is not denatured with gasoline. It's most often denatured with ethanol. Looking at the MSDS for whatever product will show what the denaturing agent is.
Every last gallon I've ever bought was denatured with ethanol.
Regarding denaturing, this is required in the US (and most countries) to prevent people from buying industrial grade ethanol and drinking it to avoid the sin tax on ethanol. By ATF regulations there are dozens of legally approved formulas for SDAs (semi denatured alcohol) and CDAs (completely denatured alcohol) to denature ethanol to make it undrinkable and tax free. To qualify as legally denatured the ethanol must adhere exactly to the ATF approved formula. Depending on the industry and application there are dozens of formulas and additives including: gasoline (used mainly in fuel grade ethanol for the auto fuel industry), ketones, other alcohols (isopropyl alcohol, n-propyl alcohol, methyl alcohol, butyl alcohol), and lots more.
So saying denatured alcohol is about as specific as saying solvent. It could be just about anything.