Are for and of interchangeable in these circumstances? Is the meaning affected at all?
He was the Minister for Education.
He was the Minister of Education.
The Institute of Medical Research.
The Institute for Medical Research.
There is no difference, except that for any given country, institute, board, or group, one of these is probably the official name, and the other one is not.
For example (from Wikipedia):
And so on.
If you use "Minister of Education" for the Australian Minister for Education, it will be obvious what you are speaking of, but it won't be the correct title, strictly speaking. So, the important thing to do is verify what the official title/name is before using it.
(On the other hand, if you are creating this title or name for your own institute, you are free to choose whichever one you want.)
In titles, the prepositions of and for can be interchangeable. What the title means is more about legal definitions rather than grammatical rules.