First beware that this is a typical case of academia varies more than you think it does. There is no general rule on how doctoral exams are done; instead, this is decided by the faculty. As a consequence, doctoral exams vary widely between universities and faculties. I know of two universities which have a joint graduate school for one field and even there doctoral exams differs extremely between the two universities.
This also applies to the terminology. So, the same term may mean something considerably different at a different faculty, in particular when it comes to official procedure. Therefore, in the following I can only write about how these terms are generally understood:
Verteidigung is arguably the most general term and the most frequently used term. Every¹ doctoral examination has at least one component in which the candidate has to face questions from the examiners and Verteidigung covers it. Official rules that are not specific to universities usually use this term when necessary. E.g., the date of the doctoral exam is usually referred to as Datum der Verteidigung.
While Disputation is just a Latin word for Verteidigung, it is used much more rarely and usually refers to a specific format of the exam, where the defendant faces questions from the examiners in public, possibly in a strict format. It can also be used in a more general sense, synonymously to Verteidigung, but at least in my experience that is rather rare.
A Rigorosum is a specific kind of doctoral exam that is characterised by featuring questions on the entire field of the candidate. It is usually not public. Many faculties do not perform this kind of exam.
A Kolloquium is a general term for a public talk, usually with questions from the audience. In the context of a doctoral exam, the candidate gives a talk on their thesis, which is usually public but may be restricted to members of the university or similar in special cases.
For example, my own doctoral exam consisted of a Kolloquium, where I talked about my thesis on dynamical systems, and was followed by a Rigorosum, where I was asked questions on my thesis but also on particle physics and solid-state physics. The entire thing was referred to as Verteidigung.
In conclusion, I strongly recommend Verteidigung unless you want to specify the mode of exam.
Finally note that the above primarily reflects the situation in Germany and the usage of these terms is somewhat different in Austria. For example, Rigorosum has a broader scope.
¹ At least as far as I know. As I said academia varies more than I think it does.