This was a tricky one to find due to when the Memoriali was set up and likely issues from translation and the possibility that the office has changed its name or has been absorbed into something else.

At the time, Bologna had the Libri Memoriali set up where notaries had to register articles with a value of 20 Lire or more to it. The term itself likely means "memorial books" if google translate is correct.

With this, it is likely to assume that the Office of the Memoriali was likely a place to register wills, death certificates, etc. for official legal records.

https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=1384&context=rmmra