Step 1: Identify reaction type.
Propanone (acetone) in presence of dilute base undergoes aldol addition (self-condensation).
Step 2: Product of aldol addition of acetone.
Two acetone molecules combine to form diacetone alcohol:
\[
(CH_3)_2CO + (CH_3)_2CO \xrightarrow{dil.\ Ba(OH)_2}
(CH_3)_2C(OH)CH_2COCH_3
\]
Step 3: IUPAC name.
Diacetone alcohol is:
\[
\text{4-hydroxy-4-methyl-2-pentanone}
\]
Final Answer:
\[
\boxed{\text{4-hydroxy-4-methyl-2-pentanone}}
\]