Is it important?
The Simpsons takes place in "Springfield" (of which there are
apparently many in the US) and they purposely don't say which one it
is, if it is any real one.
The story of "Narnia" could take place almost anywhere (the 'real
world part') and still work.
If the name of the town is important to you, use it. However, many stories take place in seemingly real places that doesn't need to be explained or proven "real" or "fictional".
Does the audience care?
I believe your audience wouldn't ask questions about the existence the town called "Williams" unless you give them a reason.
These are just two (very different) examples, but my point is that locations in stories only matter as much as you make them matter.
We (the audience) need to understand the place(s) the story takes place in. Some stories use famous landmarks etc. to play with our relation to said place(s), but in general it simply works as a location for the story to realistically take place in.
Counter-question: Do you have to mention that "it's a fictional place"?
I personally would not mention that it is a fictional place, and rather focus on making the town "Williams" come alive, fictional or not.