Not necessarily! There are a couple of reasons this may be ok. First, your company may be in a completely different type of industry from the company with the existing trademark, in which case, you should be in the clear. For example, the word 'Frontier' has been trademarked by a number of different companies, including an airline (Frontier Airlines), a telecom company (Frontier Communications), and an organic herb co-op (Frontier Co-op).
Second, you may not even be using your company's name to market your goods and services, but may instead have one or more brand names that you'll be using. For example, The Procter & Gamble Company (the company name), markets its disposable razors as Gillette ® (the brand name and trademark). In this scenario, there's no harm in having a company name that is identical to an existing trademark, since your use of it won't create any confusion as to the source of your goods or services.
If, on the other hand, you intend to use your company name to market your goods or services, AND those goods or services are in the same industry as the existing trademark, you probably want to go back and choose a different company name.