You have my sympathy. For nearly 2 years, Mil, who lives with myself and her son (my husband, her only child) has frequently insisted that there are doubles of both of us - we may share the same name as her son and his wife, but we are not them. Same goes for our kids, and even our dogs. Not only that, but her 'son and his wife' live in a house identical to the one we live in, right down to the furniture, the decoration and the pictures on the wall being exactly the same. She often asks her son if she can phone her son. She tells me about how her daughter in law, Ann, is also cooking what I am cooking for tea - and on occasion has even came downstairs after I have helped her bath and given me a blow by blow account of how her daughter in law has just made her get in the bath and wash! I can ask or tell her something and she will say 'That's funny - Ann's just said that to me'.
For the most part, I try and be non-committal now, simply saying 'Really' when she tells me what the 'other' Ann, or her 'other' son or grandchildren have said and done, and if possible I will distract. When she asks my husband if she can phone her 'son', it can be difficult when we obviously can't oblige her (as its her son she is talking to), and she can get really cross and verbally quite nasty. It isn't the best thing for eveyone, but for us, we often find that refusing to discus or asking her to go to her room when she is being offensive often works - once she is in a different room and away from any reaction, she often quickly forgets whatever it was that was upsetting her. I know this isn't the answer for everyone, though.
Its not all day, every day, it comes and goes, with some days being worse than others. And over the last 3 or 4 months I would say that its happening a lot less often - as this horrible illness progresses, I'm confident that as Marion says, it will go completely and be replaced by other issues.
Hang on in there, and hard as it is, please don't take it personally - I struggled at first, especially for some reason with her thinking like that about her grandchildren, when they used to mean the world to her, but I got used to it - though even now, when it does happen, I can still struggle with the confusion it can cause.
Take care xxxx