You work hard to build a brand and then you notice people are not finding you on Google; they are getting other results. If you name your brand after an animal, you'll have to compete with Wikipedia and other sites which are about the actual animal.
It's difficult to change your brand name if you have printed media, a domain with your brand name, social media platforms and customers who know you. You can change your domain name to your company's initials or, if you can get one, a keyword-rich domain, Use a 301 redirect to tell search engines it is a permanent move which is best for SEO.
You can change your company name and keep the same domain. Announce your name change on your website and social media and tell your email subscribers. Keep your name but add something to it to explain what you do. If your company name was Zebra, change it to Zebra Musical Instruments. Make sure you comply with all state and local laws if you want the name change official. You could also just call your company Zebra Musical Instruments and people might use the description to find you on Google.
Alternatively, you can use schema markup to tell search engines what you content is about, not just what it says. Users get better search results with rich snippets so they can find your site by scanning the search results. Unfortunately, your rich snippets may not appear in search results every time someone searches for your company even if you've added them correctly.
If you don't want to do either of these things, you can amp up your SEO efforts to rank better. It might be impossible to get in one of the top positions on the search results if your company name is Zebra. Use PPC if it's appropriate for your industry. For more information click here https://www.reddit.com/r/SEO/comments/ce8khr/fansaretypingmyartistnamewrongongoogle/.