The name for an alkyl group that contains two carbon atoms is

Homologous series contains series of compound having same general formula. The compounds differ by single parameter for example in homologous series of alkanes, compounds differ by number of carbon and hydrogen atoms. On going forward, length of carbon chain increases like methane (1 carbon atom), Ethane (2 carbon atoms), propane (3 carbon atoms) and so on.

Alkyl group is formed when one of the hydrogen atom in an alkane is replaced by any other atom. In similar way, if hydrogen is replaced in methane it forms methyl, ethane forms ethyl, propane forms propyl and so on.

Therefore, the alkyl group with 2 carbon atoms is ethyl, .

your picture is not part of the scientific method.