'Acet-' indicates ethyl, but does not offer two carbon atoms, but three.
Acetaldehyde is ethanal, acetic acid is ethanoic acid, but acetone is propanone (yes, I'm aware that there is no ethanone).
Why is propanone called acetone?
Here's a link to the first page of a book entitled, "The History of Acetone, 1600-1850" by Mel Gorman. The author points out that acetone was known in the Middle Ages and was frequently produced by heating dry lead acetate. I suspect that the "acetate" (or whatever the Latin, French or German term was) root stuck and then it was just modified a bit - to acetone - to make it distinct.
According to Fownes' Elementary Chemistry 12th Edition (pp. 676ff), ketones are obtained from the dry distillation of calcium salts of the fatty acids. So calcium acetate yields acetone, calcium propionate yields "propione" (diethyl ketone), etc. Lead salts also are stated to work.
The naming is done on the basis of the number of carbons present in the parent chain.The first member of each group is "form-". However we do not have a "formone" as ketonic groups are non-terminal.The $\ce{CH3CO-}$ groups are called "acetyl" groups(as they already contain 2 atoms of carbon) and thus the very first compound that it can form with a methyl group is propanone or acetone. However these are old-fashioned names and do not really need much intervention.The IUPAC nomenclature has logic and rightly names the compound "propanone".