Trademarked names in Google ads?

Google prohibits the use of trademarked terms in the ad title and ad copy if they receive a manual submission of proof of trademark.

However, does that prevent other companies from using our name in the keywords they are targeting?

We have a competitor that is using our name in the keywords but not the ad copy, can this be prevented with a trademark? Want to find out before going through the hassle of trademarking our name. Thanks in advance.