It seems like it would make the most sense to write your name, or even your company's name, under the designated "Name" section of your Instagram profile.
I don't suggest it though. The reason being, is that the "Name" section is one of the most searchable pieces of your profile, meaning that if someone enters a search term in Instagram's search feature, the "Name" actually takes priority over the "Username". It's kind of like Instagram SEO.
If you expected someone to find you in a Google search, would you expect them to search for your company by its specific name? You may, if you already have a lot of clout behind your company name. However, you'd more likely be banking on a user searching for the type of product you sell instead - think keywords. This is what you want to consider when deciding what information to enter into the "Name" section of your profile.
What would someone be likely to search for that could lead them to your product? How common do you think that search term is? For example, if you sell fitness apparel, you probably don't want fitness apparel to be your first search criteria because fitness is the largest industry segment on Instagram. Therefore, there will already be a LOT of accounts that have "Fitness Apparel" written in their Name section. Try to find a little bit of a niche that will be searchable, but not over-saturated. Maybe something like "Fair Trade Fitness Apparel", or "Crossfit Apparel", or even "Denver Fitness Apparel".
Put this quick trick into practice today and enjoy an increased Instagram following!
For more ways to increase your following, download my Instagram Targeting Minicourse.