If both companies offer the same or similar goods and services, and the other company has already registered the trademark federally, then you are likely out of luck. It may be best to find another name to trademark. If they have not trademarked, but they used the name first and they use the name nationally and pervasively, then you are probably still out of luck depending on the scope of their use. However, if they only use the trademark on a local basis, then you may be able to register the trademark federally and use it in those areas where they do not and have not used it before.Example: Let’s assume they have a trademark in California and have only ever done business in California. You can still register the trademark at the federal level and use it nationally. However, you cannot use it in the State of California.