Google Search is already smart enough to capture those misspellings and shows recommendations for the correct words. Assuming that your website has been around for a while, Google will show users the branded site first in the results pages so the clicks will go there.

Google figures out possible misspellings and their likely correct spellings by using words it finds while searching the web and processing searchers queries. So, unlike many spelling correctors, Google can suggest common spellings for proper nouns (names and places), and words that may not appear in a dictionary.

I usually use misspellings in my clients Paid Search campaigns to capture all the possible traffic when I see that there's a high number of searches for those variations.

I advise against buying domain names for the purpose of capturing that traffic. It will help, though, for people entering the exact domain name directly into the browser. And if you do so, make sure that they all redirect via a permanent 301 redirect to the original one, but do not use them for tricky SEO purposes.