I've also seen this used in Canadian French as a variant/shortened spelling of Pierre, and combined with Marie as a variant of Marie-Pierre (Marie-Pier).
It's very close to the French name “Pierre”. I'm surprised to see this is a Dutch name because it's quite current in Italy (even if it doesn't end with an "o")
Pier is also commonly used in Italy for compound names (like Pier Angelo), sometimes attached (like Pierluigi) and often used as a nickname for who has such names. [noted -ed]