Yes, it's very gouda!

Market Square, Woerden, originally uploaded by groggy doggy.

Of the four cheese markets in the Netherlands only the one in Woerden is authentic. Here, dairy farmers who produce cheese set the sale price with a market foreman (marktmeester) in an open setting. The other three cheese markets (kaasmarkt) are historical reproductions for tourists. They are located in the cities of Alkmaar, Edam, and Gouda.

The Gouda you find at the grocery store did not come from Gouda in the Netherlands unless it says "Noord-Hollandse Gouda." The European Union has strict standards on how place names are used on food labels. Strangely, the city of Gouda is not located in North (Noord) Holland, but South Holland - somebody should alert the PDO/PGI/TSG.