Step 1: Concept
"Allyl" refers to the group $CH_2=CH-CH_2-$.
Step 2: Meaning
The parent chain is propene. Numbering starts from the carbon with the functional group.
Step 3: Analysis
$CH_2=CH-CH_2-NH_2$. Amine is at $C_1$, double bond starts at $C_2$. Thus, Prop-2-en-1-amine.
Step 4: Conclusion
The IUPAC name is Prop-2-en-1-amine.
Final Answer: (C)