If Machine Man appeared in the movie in some form or another, sure. But since he did not, this must be a joke. Original IP first introduced in adaptations belong to the company that published said content. Warner must really like paying lawyers tens of millions of dollars to lose cases or something.
As for the name, there's nothing really stopping DC from using it. It just has to be used on a character that has absolutely zero resemblance to Marvel's Machine Man. There are, after all, several character names that are used by both DC and Marvel. "Enchantress" comes most immediately to mind, but there are several others.