1. Identify the parent ring

   The compound is a substituted cyclohexane, so the parent name is cyclohexane.

2. Identify the substituents

   From the structure, there are:

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

3. Number the ring to get the lowest set of locants

   For cyclic compounds, numbering starts from a substituted carbon and proceeds in the direction that gives the lowest set of locants.

   If we assign the carbon bearing the two methyl groups as carbon 1, we get:

   • methyl groups at $1,1$
   • ethyl group at $3$

   So the locant set is: $1,1,3$

   If instead we start numbering from the ethyl-substituted carbon as carbon 1, then we get:

   • ethyl at $1$
   • methyl groups at $3,3$ or $5,5$

   giving locant sets like: $1,3,3 \text{ or } 1,5,5$

   Compare:

   • $1,1,3$
   • $1,3,3$
   • $1,5,5$

   By the lowest set of locants rule, $1,1,3$ is the correct choice.

4. Write substituents in alphabetical order

   In IUPAC naming, substituents are cited alphabetically ignoring multiplicative prefixes like di-, tri-, etc.

   So:

   • ethyl comes before methyl

   Therefore the name is: $\boxed{3\text{-ethyl-}1,1\text{-dimethylcyclohexane}}$

5. Check options

   • A: $1$-Ethyl-$5,5$-dimethylcyclohexane $\rightarrow$ not lowest locants
   • B: $3$-Ethyl-$1,1$-dimethylcyclohexane $\rightarrow$ correct
   • C: $1$-Ethyl-$3,3$-dimethylcyclohexane $\rightarrow$ not lowest locants
   • D: $1,1$-Dimethyl-$3$-ethylcyclohexane $\rightarrow$ locants correct, but substituents not written alphabetically

Hence, the correct IUPAC name is 3-Ethyl-1,1-dimethylcyclohexane.