I'm actually hitched, and I am pregnant with another man's child. Do I need to name my significant other's name on the birth declaration?

I'm actually hitched, and I am pregnant with another man's child. Do I need to name my significant other's name on the birth declaration?
Is my main other choice to have my child daddy (he just parted ways with me) sign the affirmation to do paternity testing? We would rather not get the state in question in the event that we don't need to. He will as of now be assisting with supporting the child, and we will be co-nurturing.
I'm in Wisconsin.