Yes, it is possible to show up in the organic results. If you want to rank in the local results, you will need to create a Google My Business page. Learn how to set this up here:
If you want to show up when someone Google’s keywords related to your business, but not your exact business name, we highly recommend creating a website. It’s easier and less expensive than most business owners believe. Plus we have an in-depth guide to getting a website set up.
Hope this helps!