Concept:
According to IUPAC nomenclature, ethers are named as alkoxy derivatives of hydrocarbons. The larger carbon chain is selected as the parent chain, while the smaller group attached through oxygen is considered an alkoxy substituent.
The given compound contains a phenoxy group attached to a four-carbon chain.
\[
\mathrm{C_6H_5OCH_2CH_2CH(CH_3)_2}
\]
The group
\[
\mathrm{C_6H_5O-}
\]
is called the phenoxy group.
Step 1: Identify the longest carbon chain.
The carbon chain attached to oxygen is:
\[
CH_2-CH_2-CH(CH_3)-CH_3
\]
which corresponds to butane.
Step 2: Locate the substituents.
The phenoxy group is attached to carbon-1.
The methyl group is attached to carbon-3.
Hence, the substituents are:
\[
1\text{-phenoxy}
\]
and
\[
3\text{-methyl}
\]
Step 3: Construct the IUPAC name.
Combining the substituents and parent chain:
\[
\boxed{\text{1-Phenoxy-3-methylbutane}}
\]
Therefore, the correct option is
\[
\boxed{(C)}
\]