Step 1: Start from the precursor. Serotonin is built from tryptophan, an indole-containing amino acid, by adding a hydroxyl group and removing the carboxyl group.
Step 2: The added hydroxyl sits on carbon 5 of the indole ring and the remaining backbone is an amine, so the systematic name reads $5\text{-hydroxytryptamine}$, conventionally shortened to $5\text{-HT}$.
Step 3: The decoys come from the catecholamine and phenethylamine families. $3\text{-methoxytyramine}$ is a breakdown product of dopamine, and phenethylamine and N-methyl phenylamine are trace amines, so none matches serotonin's indole structure.
\[\boxed{\text{5-hydroxytryptamine (5-HT)}}\]