You can control if contacts are looked up by name or company. What I do not know is if changing this on the contact screen will give you the results you want on the Today Screen, but it may be worth a shot.
64 Section 2B: Using Your Device’s Phone Features
Dialing by Company Name
1.
Press Start and select Contacts.
2.
Press Menu (right softkey) and select View
By > Company. Is this Company or Name; maybe change it to name and see if it works.
3.
Press Phone/Talk to go to your Today screen.
4.
Using the keyboard, begin entering the first few
letters of the company name.
5.
Select the number you want to dial.
6.
Press Phone/Talk to dial.