Can a company claim first use for the term "Coffee2Go" if they have been operating commerce with a name such as "Coffee2Go Bardstown" and only using this phrase made up of two words, and not just "Coffee2Go"? And is Bardstown purely descriptive if you aren't able to purchase that coffee anywhere else except Bardstown? Do people have to know where Bardstown is like they know where NYC is for it not to be descriptive?
A trademark/servicemark is a brand name for kind of goods associated with a particular trademark owner, in the case of goods, or a kind of services associated with a particular servicemark owner, in the case of services, that is used in commerce (or will be in the imminent future) and has a "secondary meaning" that is associated only with the mark owner when identified with the goods or services in question. Generally speaking, trademarks and servicemarks should not be merely descriptive (e.g. Denver liquor for a liquor store in Denver).
A trade name is the proper name of a business, sometimes an entity, and sometimes a name that sole proprietor operates under (in the narrow sense, it refers only to trade names other than the true legal proper name of the business or sole proprietor). It may be descriptive and is subject to more lenient qualification. It doesn't have to have secondary meaning, and it doesn't have to be actively used in commerce. It merely has to not be a duplicate of another trade name which is already taken under the law of the applicable state of organization of the business or entity.
"Coffee2Go" and "Coffee2Go Bardstown" are both probably too descriptive to be trademarks or service marks (absent a limitation of the trademark to a distinctive logo or stylistic script), but could be a trade name if no one else is using them in the state.