What to do if I’d like to trademark my business name however, upon doing a trademark search I found another business with a name very similar to mine.

There is no definitive answer. It is possible to have businesses in different lines of business with the same or similar names: witness the number of "Acme" businesses out there of different types. The issue becomes one of potential customer confusion: the more likely actual or potential customers are to be confused as to the affiliation of the businesses or the source of goods or service, the more likely it is that the later name will be found to infringe on the existing name or to otherwise be untrademarkeable because it is not sufficiently original. The names you describe in your example are very similar; a key  factor will then be how similar the business are, even if they are not identical. For example, say your business is a spa or wellness center using natural lighting to increase health while the other business is a health  food or vitamin/supplement retailer: since both businesses are in the business of health, even if in different ways, customers could easily believe there is a connection or confuse one for the other, and hence, it is  not likely that you could use the name you want. On the other hand, say that they are a health food or supplement store while you sell light fixtures--those businesses are so different that you should be able to use the name. 
Sometimes the only way to know for sure is to attempt to trademark you name and see if it is allowed or granted.