What is the conjugate acid of NaOH using the Brønsted-Lowry definition of acids?
Your first equation is more properly written as

$$\ce{NaOH + H3O+ -&gt; Na+ + 2H2O}$$

in aqueous media. However, we can do better if we explicitly show the dissociation of $\ce{NaOH}$ as

$$\ce{NaOH -&gt; Na+ + OH-}$$

and substitute that into the first expression (note that I write $\ce{2H2O}$ as $\ce{H2O + H2O}$) to get

$$\ce{Na+ + \underbrace{OH^{-}}_{base} + \underbrace{H3O^{+}}_{acid} -&gt; Na+ + \underbrace{H2O}_{conjugate\;acid} + \underbrace{H2O}_{conjugate\;base}}$$

where we see that $\ce{H2O}$ is the conjugate acid of $\ce{OH-}$ as well as the conjugate base of $\ce{H3O+}$. The last bit - where water plays 2 roles - is due to water being amphoteric, or able to act as an acid or a base.