You dont rank on paid search, you pay per keyword, if your brand keyword generates a lot of searches and it has some value, yes you should bid on your brand

Many wonder similarly: If ranked well organically, why even run paid ads at all?

Several reasons. Not that organic traffic isn't valuable, but with paid search...

* You have much more control over what your ad says than what your organic listings say.

* You can direct visitors to the landing page of your choice, but have less control over which page shows for a given search term.

* The more your site shows on a search results page, the less room there is for competitor sites to show.

* You can get virtually instant traffic from many, many more targeted keywords with paid search.

~ Marty Foley