I think you mean "Adwords", not "Adsense".
Adsense is a Google program for publishers, which pays them for ads to appear on their sites.
Adwords is a Google program for advertisers, where advertisers pay Google for their ads to appear on Google search result pages and on other websites.
If your name is a trademark, you need to send Google a "trademark letter". In this letter, you spell-out how/if your trademark can be used by others. For example, you may permit it to be used by online stores that sell your brand, only by a specific list of authorized retailers, or by nobody but yourself.
Google will mark the keyword in their system as a trademarked term. When somebody uses the keyword in an ad, it will require a review. The reviewer will look at the ad and your trademark letter, and either approve or disapprove the ad.
Of course, you cannot restrict the use of a trademarked word in a different context. The automated system can be a pain for advertisers and result in delays, though. For example, "wow" is a trademarked term... So, if you write an ad saying "Wow, this is great!" it will be approved, but there will be a delay for approval.