It does not matter whose name is on the W-2, yours or your spouse's. The W-2 will not indicate to whose HSA the amount was sent, only that there was an HSA contribution.
This is why the screen is necessary in the W-2 interview, to establish to whose HSA the contribution went.
It seems as if you entered the W-2 and additional information correctly.
As for exhausting the funds from your HSA, this is a normal outcome for taxpayers who have gone on Medicare and who have also spent any funds left in the HSA on qualified medical expenses. Since you can never contribute to your HSA again, it's time to close it and save any fees.
It sounds as if all has been done correctly.
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