Trying to correct someone with dementia just causes confusion and panic for them.
My sister-in-law's mother suffered from dementia. She took to calling me 'Rachael' because she thought I was her daughter (30 years earlier), and my infant son was her grandbaby. We'd sit on the porch and she'd tell wonderful stories about those happy old days. We called it our 'Raising Rachael' time.
I had a similar experience with my aunt, who was my dad's only sister. There were 9 kids in their family, 8 boys and 1 girl, and my aunt was right in the middle, 4 older and 4 younger brothers.
I was named after her youngest brother, who died when he was 21 years old, from double pneumonia shortly after Mom and Dad were married in the early '50's.
I would visit her often when she was in the nursing home, and many, many time, I believe she would confuse me with her little brother. I didn't mind, it was good to hear about my family and their lives, many who were born and grew up during the first Great Depression.