While searching for people is easy, searching for companies by their names can be complicated.
If you search for “Apple” you will find:
Apple computers
But not:
The Apple company
Big Apple inc.

I have similar issues searching for people with multi-part names. For example, I have several contacts who have names that have changed after being married. Some people refer to them as “Jane Doe”, some as “Jane Smith” and some as “Jane Doe Smith”. I end up having to put “Jane Doe” in the first name field, but then when I search for “Doe” her record is not found.