IUPAC Name:
1. Identify the longest carbon chain that contains the double bond and the hydroxyl group. In this case, it is a three-carbon chain.
2. Number the carbon atoms in the chain, starting from the end closest to the double bond.
3. Indicate the position of the double bond by adding the suffix "-ene" to the name of the parent chain. The double bond is between the first and second carbon atoms, so the name becomes "prop-1-ene".
4. Indicate the presence of the hydroxyl group by adding the suffix "-ol" to the name. The hydroxyl group is on the third carbon atom, so the final name is "3-hydroxyprop-1-ene".

Common Name:
1. Identify the parent chain as a three-carbon chain with a double bond.
2. Use the prefix "allyl" to indicate the presence of the double bond.
3. Add the suffix "-alcohol" to indicate the presence of the hydroxyl group. The final name is "allyl alcohol".

Note: The IUPAC name is the preferred method of naming organic compounds because it provides a systematic way of naming compounds that is unambiguous and universally recognized. The common name is a more informal way of naming compounds that is based on historical precedent and may vary between different regions and languages.