I own a retail business that designs and sells stationery products. After being in business for the past 5 years, we are rebranding our company. I would like to trademark our new company name. For example, let's call it "Leaf & Wool". There are no other registered trademarks with a similar name in the same industry, however, another company exists with a similar name. For example, let's call the other company "Leaf Avenue Paper Company". The other company does not have a registered trademark for their name, but they have been in business for as long as us. Would I be able to register a name like "Leaf & Wool", if a company already exists with the name "Leaf Avenue Paper Company"? If we are approved for the trademark, could the other company file a lawsuit because they had the name first?