Can I use photos of an unbranded product I own in my portfolio?

When creating a photograph of a 3-dimensional object, you are not at risk for violating the copyrights that rest on that object. This is primarily, because you are not creating an actual copy of the object, but merely a 2-dimensional representation of it.
Having the photograph of a backpack does not give you an item with the identical function of a backpack and therefore it can't be a copy.

However, there are other Intellectual Property rights that you need to take into account. The most important ones are Trademarks and Industrial Design Rights.

If an object has a very distinctive design (that is more than utilitarian), then it is likely to be protected by Industrial Design Rights, which means that you are not free to reproduce the design of the product, not even in a completely different medium, such as a photograph.
This, for example, holds also for buildings designed as a one-off by an architect, where you can´t just take/publish pictures of the building without permission from the architect (unless it is more of an overview shot with the building in its surroundings).