A: I suppose your question is if two companies with same name or trademark can coexist. Well there different considerations to make. In general terms two trademarks can exist if they are not substantially so as to cause likelihood of confusion. However, this is a legal term, one would need more information to give you a real answer. Additionally, for purpose of your trademark filing, if the other business is not opposing to the registration you may have a chance of being successful. Like my colleague said more information is necessary.
I wrote this note which could be useful for you:
A: I general terms when two business of different industries have the same name this is not a problem if they as so different that consumers will not misleaded. That said, in the world of trademarks the airline could do two things if it discover that another business is using its name. It could send a cease and desist letter, or it could oppose a trademark registration of the same name before the USPTO. However, to be successful or to have a real possibility of winning in litigation the airline would have to prove consumer confusion or a substantial likelihood. Additionally, the airline would have to prove that it is so popular or well known that a consumer could be misled. This means, that the airline could have no real possibility of preventing another from using its same name. Nevertheless, if the airline has more money for legal fees, it may has a chance to drag another to a litigation it cannot win because of lack of resources to pay an attorney for a good defense. At the of the day, it all depends of the difference of the two business and of getting legal counsel ti determine risks and how to handle them.