Identify the parent ring

The compound is a substituted cyclohexane, so the parent name is: $\text{cyclohexane}$

Identify the substituents

From the structure/options, the ring has:

• one ethyl group
• two methyl groups on the same carbon, i.e. gem-dimethyl

Choose numbering to get the lowest set of locants

There are two possible ways to number the ring:

• Ethyl at carbon 1 and dimethyl at carbon 2 $\Rightarrow$ locants: $1,2,2$
• Dimethyl at carbon 1 and ethyl at carbon 2 $\Rightarrow$ locants: $1,1,2$

By the lowest set of locants rule, we choose: $1,1,2$ since this is lower than $1,2,2$.

So the numbering is:

• two methyl groups at carbon 1
• one ethyl group at carbon 2

Arrange substituents alphabetically

In IUPAC naming, substituents are written in alphabetical order, ignoring multiplicative prefixes like di-, tri-, etc.

So:

• ethyl comes before methyl

Therefore the name is: $\text{2-ethyl-1,1-dimethylcyclohexane}$

Check options

• A: 1,1-Dimethyl-2-ethylcyclohexane
  Locants are fine, but substituents are not written in alphabetical order.

• B: 2-Ethyl-1,1-dimethylcyclohexane
  Correct locants and correct alphabetical order.

• C: 1-Ethyl-2,2-dimethylcyclohexane
  Gives locants $1,2,2$, which is not the lowest set.

• D: 2,2-Dimethyl-1-ethylcyclohexane
  Gives locants $1,2,2$, not lowest; also order not preferred.

Final answer

The correct IUPAC name is: $\boxed{\text{2-Ethyl-1,1-dimethylcyclohexane}}$

Hence, the correct option is B.