It reminds me of the fallacy of the excluded middle but it’s more specific than that and relies on something analogous but still different I think:
What do you call it when someone says: “You’re not in favor of my particular option so you’re in favor of nothing at all.” That is, trying to portray one’s opponent as being in favor of no standard or no action because he disagrees with one particular standard or action.
Example 1): If you’re not in favor of restricting marriage to a man and a woman, then a man will be able to marry a dog.
Example 2): If you don’t want this state intervention in the economy, then you want to leave it all up to the market.
Now, it is possible that someone who is not in favor of restricting marriage to a man and a woman would indeed want no restrictions so that a man could marry a dog. It’s also possible that someone who is against a particular intervention is against all of them. Yet it doesn’t logically follow. It’s as fallacious as saying that because someone is against the Westminster parliamentary system, they’re against all government.
So, does it have a name? It’s not really about there being a middle or denying that there is.