Yes, if you're filing as Married Filing Separately, you still have to give your spouse's name and SSN. Be sure to indicate your MFS status in the MY INFO section.
You certainly can delete her W-2, though. Type 'W-2' in the Search area, then 'Jump to w-2'. When the summary page opens, choose DELETE for her W-2.
Here's more info on Changing from MFJ to MFS.
@tsciortino