Windows cannot have two C drives, so the second drive will be seen as D.
When your clone is finished, and you remove the old C, the temporary D drive will become the new C.
The cloned drive would not function as D anyway, because all the software on it (as it's a clone) is pathed to C: locations. There are ways to force the new D to stay as D, but that takes extra effort. It doesn't happen by default. And in order for it to function, Windows would have to be installed fresh as D: instead of C:
In other words: No worries.