Okay, let's see... it's been a LOOOONG time since I've had organic chemistry, let's see what the old brain cells will do here...
CH3CH2OH
That would be...
ethanol. That would be the complete organic chemical name.
This is a straight-chain hydrocarbon, with one alcohol group (-ol). Because there are only two carbon atoms in the chain, you don't need any numbers to indicate where in the chain the alcohol group is.
If it were a longer chain, you would need a number to indicate to which carbon atom the alcohol group is attached. For instance, I can make three alcohol groups from a five-carbon chain:
CH2OH-CH2-CH2-CH2-CH3 (Would be 1-pentanol, I believe)
CH3-CHOH-CH2-CH2-CH3 (Would be 2-pentanol, I believe)
CH3-CH2-CHOH-CH2-CH3 (Would be 3-pentanol, I believe)
Then it gets more complex if it's not a straight chain:
C-C-C-C
***|
***COH
Would have the same number of atoms, but have a totally different name. (Oh boy... would it be... uh... 2-methol butane? That's a WAG, BTW.)
In any case, the answer to your original question is that the complete organic chemical name for drinking alcohol is Ethanol. Ethanol is not a shorthand for a more complex/complete name, ethanol is the complete name.
Edit: I needed asterisks to move the lower chain from the left margin. And changed 1-methol to 2-methol.
Edit again: In my example above, you wouldn't need the number 2 to indicate where the methol group attached, since there's only one place for it to attach. (If it attached to the end of the chain, it becomes a straight chain pentanol.)