They made a movie about George Bush being assassinated. Presidents are in the public arena like no others and I don’t think they are provided such protections against being made characters in novels, or unflattering skits, or movies or political cartoons, or any other media where someone might choose to portray them.
But this is a very specialized area of law that might not have even been addressed yet. So unless someone here is an authoritative attorney in this field, no one here can provide definitive answers.
So I’ll say again, I doubt a president, or a candidate for president would be granted such trademark protection for their name. And, as far as politics goes, her application says nothing more than use to provide information about political elections and issues, a far cry from being a candidate, let alone president.
Say it all you want. The trademark appears to be on track to being granted whether you like it or not.
If you can’t see the reason that she might want such a trademark, I can’t help you.
You need to read up on what the nature of a trademark is, and its purpose and limitations. Try the USPTO website, Wikipedia or any one of hundreds of IP law firm sites. So far, I’m sorry to say, you are utterly clueless.