The correct IUPAC name for CH2 = CHCH2NHCH3 is

1.  Allyl methylamine

2.  2-Amino-4-pentene 

3.  4-Aminopent-1-ene

4.  N-methylprop-2-en-1-amine  

Hint: Priority must be given to amine group not double bond.

In the given compound numbering must be start from right to left because amine give higher priority than double bond. The numbering in the compound is shown below

C3H2 = CH2CH12NHCH3 
The parent chain contains thre carbon atoms hence "prop" is used for that, for double bond "en" is used as suffix and for -NH2 group amine is used as suffix.
The IUPAC name of the compound is as follows:

Hence. option (d) is correct.