If you searched for your company's name and they use dynamic insertion, your search will appear, for example in their title.
What you can do is to ask for brand protection, so they would be forbidden to bid for your company's name.
It is just a possibility, I couldn't understand the exact details of your situation

Does anyone know if you can stop adwords advertisers from using your company name in the title of their ads?

For the full story, Liane, it's probably best to reference the appropriate sections of the AdWords Help Center.

Starting here:

Editorial and Site Guidelines
[adwords.google.com...]

There you'll find:

What is Google's trademark policy
[adwords.google.com...]

How do I file a trademark complaint in the U.S. or Canada?
[adwords.google.com...]

How do I file a trademark complaint outside the U.S. and Canada?
[adwords.google.com...]

Hope that'll help.

AWA