Well, since the clasts are more rounded than angular, conglomerate would indeed be more correct than breccia. The clasts are not all of the same rock type, so we would call it 'polymict'. They're also very variable in size so are from 'unsorted' sediment. There is also sufficient cementing matrix that we would call it 'matrix-supported'.
Usually, these types of rocks are just generically called 'pudding stone' and may be additionally specified by clast/matrix type... eg 'chert in sandstone conglomerate' or whatever. Whether it also has a more specific localised name than that will very much depend on where you found it.
Cool specimen.