I've seen "Columbia" used in poetry as an alternate name - is there any evidence that this was given consideration, or is just a flight of fancy?

While I don't know if it was considered as an official name, Gordon Wood argues in "Empire of Liberty: A History of the Early Republic" that the term "Freedonian" originated in post-Revolution America as a way for Americans to describe themselves. That could possibly be considered an alternative name, depending on how generous you want to be.

You're questioned is kind of flawed, the Declaration only sought to sever ties between the 13 colonies and Britain, it did not establish a new government. The articles of confederation were the first attempts at a united governing body, but ultimately failed, and it wasn't until the signing of the constitution that the United States of America as a nation became a thing. Not trying to be a dick, but seeing as this is a sub intended for learning I thought I could try to make a secondary lesson out of the mistake within your question.

Follow-up/related question:

Was there a term that was used to describe the collective north American colonies before the "United States"? That is, if I were in pre-revolution England and I wanted to refer to our colonies in NA was there a name/term for this?

edit-for-clarity: I'm specifically interested in what someone outside of the colonies would have called them. Not what the colonists would have necessarily called them. (if, indeed, there would have been a difference)