No, cheese is not seasoned by default.
Some cheeses do contain salt, or herbs, or spices - but any spices, seasonings, or salts are considered as much a part of the finished cheese as the starter culture or the milk. It would be like asking if you can get pickles that are unseasoned, when it's the vinegar or spices in the brine that makes them pickled, or like questioning the salt or spices in cured meats - the whole process is what makes it what it is, and absent those ingredients and processes, you don't have the specific cheese.
Since you were asking about "unseasoned" cheese as just milk and culture, you might be interested in knowing that there are in fact multiple cheese cultures, specific to a lot of different kinds of cheese - much like wine yeasts, it is one of the major components and the one that decides which cheese is going to be what. Most cheeses also use a different curdling agent, often rennet, or else citric acid - which is different from the yeasts which give the cheeses flavor. Other specific parts of the process define different kinds of cheeses, so that a cheese missing some piece of its process is, in fact, a different cheese - like salting to bring out moisture, adding one fungus for blue cheeses, and a different one for brie cheeses.
A gouda cheese, for example, needs to have the curds washed (removing lactic acid for a sweeter cheese), and soaked in a brine solution which gives its rind a characteristic taste, and is further divided based on aging. It also depends on being a cow's milk cheese, a yellow cheese, rather mild and sweet, and based on the traditional Dutch methods of production. Cheddar is also a yellow cow's milk cheese, named for the cheddaring process (laying curds crosswise for texture), and depends on being sharper and acidic in flavor. It is also a much more common process, so cheddar is produced all over in a wide variety of cheeses, unlike gouda which is more limited in what counts as one. A mozzerella and paneer are both made with acid, but mozzarella uses citric acid and also has rennet and is stretched for texture, and it is moister so it will melt, while paneer is made with lemon juice and pressed dry and dense to hold up to handling and to stay firm. Which is "seasoned", and which "unseasoned", when they are both so different? I don't know. And paneer and feta are made with very similar processes, until the cheese is brined... except the milk is very different, which is how you get a soft fatty feta (goat and sheep milk) and a firm chewy paneer (cow milk) even before the salty brine is added.
I suppose I should mention that there are cheeses which have flavors added - like garlic cheddar, or pepperjack, or anatto seed to make yellow cheddar, yellow, or any number of herbs and spices. Again, I think this still isn't the same thing as "default seasoned or unseasoned", because it is about creating a different product. A cheddar with garlic doesn't taste the same as a garlic cheddar to me, a plain cheddar isn't the same is a "garlic cheddar without garlic". You can disagree, or you can prefer or avoid cheeses with added flavors, but that's my take on it.
And now, getting back to your original point. If you buy a gouda, what you should be getting is a chunk of gouda cheese, not a "gouda flavored chunk of generic cheese". If you get a smoked gouda, on the other hand, then the cheese is being advertised as changed from the original, with smoke flavor added to the basic gouda cheese (and other changes coming from the process of smoking, etc). Specifically, the flavors in gouda are created through the interaction of the milk, the process, the cultures, and the aging. If you're interested in knowing what is in a cheese, ingredient lists or nutrition labels will help. If you can see the cheese, you can look for flecks of herbs, or whole spices, or other textural signals that might show other ingredients in the cheese. Most such cheeses will advertise these additions, though, as they are different products with different appeal. Any cheese with an unmodified label should be considered "unseasoned" or regular cheese for its kind - this might not help much when it comes to cheeses where the addition is considered default (like annato in yellow cheddar, or penicillium mold in blue cheese), but it should help you weed out the dill havarti from the garlic havarti from the plain one - and you'll just have to take your chances with the pepper jack vs montery jack, or yellow vs white cheddar.
So, when I'm saying there's no unseasoned cheese, what I'm saying is there's no generic basic cheese which gets flavored or processed into all the other cheeses - it isn't a base material to be seasoned into something else. If there's a flavor to "unseasoned cheese", it is plain milk - or not even that, because the flavors also come from what kind of milk, and what kind of animals (cow vs sheep vs goat is a really big difference), and seasons and years and conditions these milk bearing animals lived in. The flavors also come from the starter cultures, and processing, and developing the flavors (as by aging, brining, smoking, washing the curds, or the rinds, in all sorts of substances, adding herbs and spices).