Is the business new? So is not rebranding.
Changing my your company's name to your own can set you back a bit. This is because a name is intended to be a conveyor of trust, are you an authority in your industry? Local Market? If so then it should help boost sales. If people are more familiar with the current company name specially since you are a reseller (if you are) of third party solutions and your value is in implementing those tools, you could be best keeping the current business name. For example, an insurance agent working under farmers brand conveys that he is just an agent. While John Smith insurance could sway either way depending on context in which a consumer crosses your path. They could assume your products are your own, if they are not that (could) lead to loss in potential customers. In the financial industry this is not uncommon however and if there is no brand to start with your efforts are the same. You have to build trust, with that you build authority and with authority you get to claim your name as a brand and trustworthy service provider.

A brand is not a logo. If people could care less if you change the name then you have no brand just a business logo and tax alias. Become a well known expert in your local market as you build your name sakes service... :)

There are ways to become an expert and ways to leverage that online. Some of us here have done that for ourselves and or for others.