Using a name mapping for those dialogs is almost certainly going to result in an ambiguous object recognition warning when both appear on the screen at the same time. However, TestComplete can distinguish them by index. In my example below you can see I have two Explorer windows open at the same time. The Object Spy shows an index that distinguishes them.
If I wanted to click on the first one, I would address it in the keyword test using the index "1" something like this:
If I wanted to work with the other Explorer window then I would use the index 2. As long as you use the correct index TC should be able to distinguish the two dialogs allowing you to target the desired one.
