When you create a picklist, there is a Name field and a Display Name field. The Name field is sort of a unique identifier, like PersonName and the Display Name field is the natural way a User would see the value, like Your Name.
Unfortunately, when you build a Power App, the Picklist displays the Name field. Users went to see a friendly field name, not the field the database designer uses.
Hi All - sorry for the delay in updating this suggestion - this is now available in the latest version of the Common Data Service.
Display names for Option sets (replacement for Picklists) are now used in data tables, forms and drop downs.
You need to be using an environment created after the 3/21/18 to see the new features - if you're using an existing environment, you'll be prompted in the coming weeks to be upgraded to the latest version.