In any case you should just have one domain name as the main domain name: the more common one for your target audience (the other one should be permanently redirected) which is most likely the more common one in the Google index as well. You should avoid "duplicate content".
If one is searching for a common name (or term) with two possible spellings, Google will usually take care of that and suggest the more common version (for example if you search for "flatly" it will suggest "Did you mean 'flatley'?").
If you expect people to search for both possible spellings for less common words, those that Google doesn't map both ways, it's not only a matter of domain names but of what's on the website, so I'd make sure to include both spellings in important positions on the page.