Person with dementia seems to know certain people are family, but isn't sure who they are?

Great answer! It makes lots of sense (to me).

My grandmother would tell my Dad (her son), "I have a son named Jim".

A resident in a LTC facility thought he was on his ship during WWII. Whenever a "Department Meeting" (for heads of nursing, dietary, housekeeping, therapy, etc) was announced over the facility's loud speaker, the resident would go to the meeting because he was a "Department Head" for his section of the battle ship. More than once we had to redirect him to "an urgent problem below deck that required his attention immediately"--he would leave the meeting only if he received permission from "the Commander" (AKA Facility Adminstrator).

Makes sense. I did try this with him (Hi, I'm so-and-so. Thanks for having me over). His reply was "Of course, I know you!" I wasn't clear if he knew me from the get-go, if he knew me as a result of me giving him my name, or if he still didn't know me but was pretending like he did. I agree with you that it certainly can't do any harm to work my name into the conversation. If it helps, then it helps. There was one occasion where his wife had just finished telling me that he no longer knows anyone's names anyway. However, she'd no sooner said that and he called someone (correctly) by name. I really think some moments are better than others.

Thanks for this information. I guess it's a glimmer of what they can still remember in terms of the person being someone they know, but can't correctly identify them. I agree that correcting him seems futile.