The first thing to do when constructing a systematic name is to find the parent structure - be it a cycle, or in this case an acyclic chain.
You choose the parent structure with the most skeletal carbon atoms - that is the longest chain. Here the longest chain in 2 carbon atoms so we start with a parent chain of ethane.
Ethane been substituted with -$\ce{NH2}$ and $\ce{O}$ which describes an amide group. So combining the amide suffix and the ethane parent, we get ethanamide.
NB: carboxyamide group
A carboxyamide group includes the carbon atom, so if you incorrectlydeclared the $\ce{CH3}$ group as the parent methane, you could say it is substituted with a carboxyamide group and would be called methanecarboxamide.
An example of the correct use of carboxyamide is cyclohexanecarboxyamide (pictured below). Here the cyclohexane ring system is the parent and the can be described as carboyamide substituted.
The minutiae of systematic naming is described in the IUPAC Blue Book. Here the relevant rule is P-44.3.2