I typically deal with dots at the same place as a single dot and, when clicked, open an infowindow/infopanel that will let people see all of the points’ data.
ie you do need to deal with this issue (by default, no mapping library will do it for you) - and most clustering librairies (or at least their default settings) will also not solve this for you.
The ui for what happens when a point (or even a cluster) is clicked but that point contains more than one point’s worth of data is its own separate problem basically