While it may be seen as a different question the answer has largely been dealbt with here Google thinks my domain doesn't exist or is misspelled when users search for it
The fastest way to correct this is to make your site the authoritative for your company name. The sooner your site is seen by Google to be the destination for your (misspelled word) company name the sooner Google will be direct people to your site for that keyword search instead of offering them alternatives.
You may be tempted to include the non-misspelled version of the company name in your pages as a keyword, but there's two problems with that:
- if it is a very popular word then you enter into a highly competitive market for that keyword, one which you may not be able to win and so consign your website to relative obscurity. I am assuming that was possibly your reason for choosing a misspelling in the first place - to stand out from the crowd.
- you set back your attempts to gain Google's favour for your misspelled keyword by diluting focus and either make it a slower process to achieve notoriety for your misspelled name or potentially even negate it.
In the meantime, you can search Google for site:yourdomainname.com to see what links are already in Google's index for your site, or click the "Search Results" button and the All Results dropdown and select "Verbatim" to get specific results related to your misspelling.
So again it comes back to making your site the best it can be for your keywords - quality unique content, good titles and semantics etc.
The good news is, since your company name is probably quite rare or even unique, you will have very little competition, and once Google as realised that the misspelling is a real 'thing' you are likely to receive Sitelinks fairly early on even without much traffic.