Just use a regular dictionary (also dynamic set) and attach a counter to each entry. The insert operation then finds already existing entries and can increase the counter; similarly for delete.
If you want to search the literature, some sources (e.g. Algorithms by R. Sedgewick and K. Wayne (2011, 4th ed)) call the abstract data structure for multi sets a bag. This notion seems to be used in practice as well.
Note that some implementations will assume that you assign data to keys, and that the same key can occur multiple times with different data. In this case, using a counter is not enough, so these may not directly do what you want (since they may not even bother to detect duplicate keys).