How do you name this: (CH3)2CHCH2N(CH3)2

is it N,N-dimethylisobutanamine
or N,N-dimethylisobutylamine

I found both answers on another site, but the first answer you suggested looks to e more correct by the other website's information:

CH3-CH-CH2-N-CH3
........|..............|
........CH3........CH3

The longest carbon chain that includes the nitrogen is 3, so this is a propyl compound.
You use the lowest carbon number to designate the location of the nitrogen, so this is a 1-propyl amine.

Sin the nitrogen is completely substituted this will be a tertiary amine.

Then count to the carbon with the additional methyl group.

It's on carbon #2

2-methyl,1-propyl,N,N-dimethyl amine

There are a number of less correct names, like
iso-butyl, dimethyl amine