Based on my personal experience and travels, it is most often the residents of other countries that refer to the U.S. as "America", not the residents of the U.S. themselves. When it is the U.S. residents saying it, it usually in mixed company with people from different countries.
As an example - I regularly have online conferences and training sessions with clients from all over the world, most of which require translators. When the topic came up about where I am located, I would respond with "the U.S." or "United States", only to have the translator repeat that as "America".
After a few months, I gave in and just started to respond "America". What I learned was that everyone on the line would know exactly what I said and what the question was, without having the information translated back to them.
So, if you are asking me to stop referencing "America" in my dealings with residents of other countries - then I am afraid that is a bridge we are not going to be able to cross together.
However, if you are in fact talking about WT and location name fields, categories, etc. - then I believe that WT already has policies on the usage, although it may not be specifically spelled out to say "Don't call it America".
For instance, the Location Field Style Guide states that:
Abbreviation of country names is acceptable as long as the abbreviation is standard and is recognizable.
"America" is not a standard abbreviation, but it is recognizable. Does that mean it should be used? Of course not, the correct abbreviations are either "U.S." or "USA".
Category Names for Regions states that:
Categories for modern countries use the short form in common usage, as in Category:Australia not Category:Commonwealth of Australia.
"United States" is an acceptable short form, while "America" is not.
So if you run across America being used outside of G2G in a profile field, then feel free to dive in and help clean it up.