[pirateking]

Humans have done just fine for a long time managing their own mental namespaces. Paper already means different things in different contexts before either of these apps - "I am writing a paper", "have you read today's paper?", "have your papers ready for inspection". There are also many different brands and types of paper with very different material properties and use cases.

Choosing an already in use word for any new publicly accessible thing complicates the global namespace a little more than it already is, but if it is the name you really wish to give it, sometimes a little distributed parsing overhead is better than the alternatives - trademarking "paper" or calling your product "Payper" instead.