I found out today that there is a character in a movie (from, like, 1989) with the same name (first and last) as my antagonist. This name is rather common. The last name is, I believe, in the top 20 American last names. There's (if you go type in the name on Instagram, or even google) a lot of people with that name. That's okay, right? I mean, you can't trademark a common name, can you? Also, if it makes a difference, my antagonist does have a middle name that is mentioned.
Honestly, I'm no legal pro... or any other sort of pro, but the chances are that a bunch of fictional characters as well as actual people share a name that common, so I'd assume you're safe. If not I better watch out. My story has a James Walker and a Joseph Dean. Er... unless of course either names have been trademarked.
You can technically use a name even if a name is trademarked - because a trademark is, surprise, tied to a certain trade. For example, Sarah Palin has trademarked (servicemarked) her name for "educational and entertainment services, namely, providing motivational speaking services in the field of politics, culture, business and values," as well as "information about political elections" and "a website featuring information about political issues."(Source) So, unless your char is professional politician or motivational speaker, you can still name her Sarah Palin. And perhaps even if she is - don't know, is there precedence about someone claiming trademark violation by a fictional character? That'd be hilarious. And if there is, you can always argue that it's satire.