How can I search my contacts by business name on an iPhone?

This has been going on for awhile now through various iOS.... I use apple contacts and have many contacts where ive entered a person's name along with the business name in the contact card. I have not entered any custom fields. I have first name, last name and company fields by default. On those cards, with both a persons name and business name, when I search by business name on the iPhone , by swiping down on the Home Screen to make the search bar come up, I get no search results. But, when I search by name, I get the expected results. The problem is I'm bad with names and more likely to remember a business name rather than a person's name. is there a way to get the results to show when searching by business name for those cards that have both person's name and business name used in the contact?