Re-naming is re-branding. And re-branding requires an investment of time and money. However, you could change your business name and still maintain your rankings. Having a solid SEO and PPC strategy will help you. Just because you would drop the geotargeted location from your business name doesn't mean that you won't be able to rank in a top spot.

I would recommend the old advice of putting together a business plan around the new brand you're envisioning, identifying specific, measurable goals you are looking to achieve.

Then I would work backward to identify everything you need to do to develop, or enhance, the brand to meet the standards of your vision. Financially, does this change make sense? Will it improve your customers' experience?

This is a deep topic, but hopefully all of our comments can help you arrive at a decision you're confident with.

-Diane