Step 1: Understanding IUPAC naming.
The structure \( \text{H}_2\text{N-CH}_2\text{C=CH}_2 \) consists of a propene backbone with an amine group attached to the first carbon. The numbering of the carbon chain is done from the amine group to ensure the lowest possible locants. The double bond is at position 2. Hence, the name is Prop-2-en-1-amine.
Step 2: Analyzing the options.
(A) 1-propenamine: Incorrect. This name suggests that the amine is on the second carbon, which is not correct.
(B) 3-Aminopropene: Incorrect. This name suggests that the amine group is on the third carbon, which does not reflect the structure.
(C) Prop-1-en-3-amine: Incorrect. The numbering of the carbon chain is incorrect. The double bond is at position 2, not 1.
(D) Prop-2-en-1-amine: Correct — This is the correct IUPAC name, where the double bond is at position 2, and the amine group is on carbon 1.
Step 3: Conclusion.
The correct answer is (D) Prop-2-en-1-amine.