Branded search makes up the largest part of search traffic to your site. Though your business name may rank number 1, Google serves up other results too. You can influence those results.
When a user searches your brand name, make use of the other organic real estate: link build to other source materials that helps you.
Link build to authoritative blogs and news sites that write about your company. Showing positive coverage of your business adds to the legitimacy of your brand. This also saves the user from deep research of your brand, as it is served up to them. Users are more engaged with such information, making your business stand out in their mind.
If you don't have other credible news sites writing about your business, link build to your social media and YouTube pages. These are channels where you can control the message; just make sure the content is rich and engaging.
These sites already have great domain authority with a wildly diverse link graph. As such you can get away with aggressive anchor text focused link building to your brand name. Even after Penguin, aggressive tactics such as article spinning or profiling can be utilized on highly authoritative websites with pages mentioning your brand. But to be sure, investigate their link graph. You don't want to be penalizing anybody else's web property.
By ranking other websites that speak to or about your business, users engage with information that makes your brand stand out.
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