The correct IUPAC name for \[C{H_2} = CHC{H_2}NHC{H_3}\] is:
A.Allyl methylamine
B.2-amino-4-pentene
C.4-aminopent-1-ene
D.N-methylprop-2-en-1-amine

Hint: One can solve this question by keeping in mind the IUPAC nomenclature rules. If nitrogen is present, it can be either amine or amide functional group. Parent carbon chain can be determined by calculating the number of carbons in the longest carbon chain.

Complete step by step answer:
If organic compounds contain one principal functional group then the longest continuous chain of carbon atoms having that functional group is selected. Functional groups are specific substituents in the molecules which are responsible for the characteristic chemical reactions of those molecules.
The IUPAC nomenclature of organic chemistry is a system of organic chemical compounds in nomenclature of chemicals as stated by the International Union of Pure and Applied Chemistry. Informally we call it the Blue Book. The book mentions certain rules for naming of compounds having functional groups.
As per IUPAC rules, the first thing is to select the longest continuous chain. In the given compound, the longest chain has three carbon atoms, so its root word is prop. We will start the number from carbon which is next to nitrogen to the left. This gives us a double bond on second position and can be written as 2-ene.
We can see that there is a methyl group attached to the nitrogen of amine functional group, so we can write it as N-methyl. Putting the suffix as the name of the functional group, we end up getting the correct IUPAC name of this compound as N-methylprop-2-en-1-amine.

Hence, the correct option is (D).

Note:
The Amine group is represented by \[N{H_3}\] . When we replace the hydrogens attached to nitrogen with any other compound, it becomes either primary or secondary or tertiary amine with respect to the number of hydrogens replaced. In our case, two hydrogens were replaced, so the compound is secondary amine.