Uniform Prior on Normal Mean with Known Variance Implies Truncated Normal Posterior?

Let's say I have a uniform prior $$\mu \sim \mathcal{U}(a,b)$$, a normal likelihood $$y|\mu \sim \mathcal{N}(\mu,\sigma^2)$$ with known variance $$\sigma^2$$, and one observation $$y$$. Is then the posterior $$\mu|y$$ a truncated normal distribution with parameters with parameter $$\mu=y$$, $$\sigma=\sigma$$, $$a=a$$, $$b=b$$?

Yes: $$p(\mu \mid y) \propto p(y \mid \mu) \, p(\mu) \propto \mathcal N(y; \mu, \sigma^2) \, \mathbb{1}(\mu \in [a, b]) ,$$ where $$\mathbb 1$$ is the 0-1 indicator function. This is exactly (up to a multiplicative constant) the pdf of the distribution you said.