I created a myDATES range  with several thousand dates, and your unmodified code
works perfectly for me. It sounds like Min and Max are only looking at the first
cell in your range. If the name is defined via VBA, maybe it's not including all
the cells you think it is. If this is part of a longer procedure, maybe the name
is being re-assigned to the single cell somewhere, before you are calling Min &
Max. Why not stick a statement like

MsgBox Range("myDATES").Address

just before your Min/Max calls, to see what cells are included in the search
range?