You already got some good answers, but I think there is one more important point which is mainly a language issue and which should be mentioned - in particular since your main concern seems to be about the name of the program.
Apparently, "Information System Management" in the question refers to this program at TU Berlin. The issue is that the English name of the program probably gives rise to different connotations than its German name, which is simply "Wirtschaftsinformatik". Since the majority of users of this site is unlikely to speak German, here is a brief explanation: "Informatik" is simply the German word for "computer science", and "Wirtschaft" is a quite generic German word which can mean various things from both business and economics.
There has been somekind of trend in Germany during the last decades to take any classical STEM program X, replace a few of the contents with anything related either to business or economics, and then call it "Wirtschafts-X". This often raises some issues and misunderstandings when you try to translate the name of such a program to English.
I think if you apply for a PhD in Germany or in German-speaking countries, the name "Wirtschaftsinformatik" is unlikely to cause you many problems as long as you have taken courses which fit the profile of the PhD that you'd like to do. If you apply in other countries and use the English notion "Information System Management" though, you might want to explain this a bit in your application.
But anyway, the most important thing will be which courses you take. The details of the program at TU Berlin are specified in the "Studien- und Prüfungsordnung" (link; in German). I've only looked very briefly at it, but what would make me a bit wary in your case is, for instance, that all the modules "Machine Learning 1", "Machine Learning 2", and so on, are listed in the list "Fachstudium Wirtschaftsinformatik", but not in the list "Fachstudium Informatik". This might raise the question whether these courses also treat the theoretical foundations of this topic in detail, or whether they mainly focus on applications. The table on the bottom of page 352 shows that a considerable number of credit points in the program are assigned to the fields "Wirtschaft und Management" and "Wirtschaftsinformatik", and only a few are assigned to "Informatik".
I don't know how much theoretical background is typically required for a PhD in artificial intelligence - but it might be worthwhile for you to briefly double-check whether the "Wirtschaftsinformatik" program you're interested in leaves sufficiently many opportunities for in-depth theoretical courses, or whether it focusses mainly on applications.