For your Facebook business page…
Step 1: Choose your Facebook business page name carefully. If possible, use the same name that the rest of the internet associates with your business. Remember, consistency is the best policy.
Step 2: Choose a username. The @... that links your name when your page is tagged. This edits your Facebook.com /URL. The username can be found in the About section. If possible, be consistent with usernames on other social channels.
Step 3: Verify your page! This is the lovely little check-mark that you see next to some business page names. This helps pages rank higher in Facebook search. To verify your page, go to Settings→ General→ Page Verification. Follow the prompts from here that are required from Facebook. Once you have one Verified page, be sure to “merge” any additional pages that represent your business.
Step 4: Fill everything out—I’m going to repeat this one more time—everything. Take some time to do this because it’s important for Facebook search when recommending your page. Go to About, click Edit Page Info and review each section starting with General. Be sure to clarify your intent and sprinkle some relevant key words here.
Step 5: Hashtag it up! Try to create a hashtag that is unique to your brand and don’t be afraid to join other trending hashtags in the social world to help your posts gain organic visibility.
If you use your personal Facebook page for business branding…
This is a hot topic lately. Have you noticed that you see your friends posts more so than business pages that you Like? This is because Facebook is more likely to show friends content before business page content.
If this is a route that you explore and you want to be found on major search engines, you can make your Facebook profile search friendly. In your personal page, go to Settings → Privacy →Who can look me up? Here you can choose where you want to be found. Remember, this is a personal choice.
You also have choice in Privacy to go public and turn on Followers. Remember, if you choose to keep your personal page for personal use, there are still plenty of strategies to get ROI out of your business page.
*Please note that a good social media strategy has not been claimed to be a part of search engine algorithms like Google for ranking websites. What I am discussing above is related to Facebook search only.