I've had people come up to me before speaking to me in ways similar to what you're saying but I actually ask them who they are and who they think I am and a lot of the time they realize I'm not who they thought I was. You can't just assume the reason they thought they knew you was because you are multiple. That's illogical.

If you have more legit reasons to be worried about dissociative disorders then go ahead and get a second opinion but memory issues is a symptom of hundreds of disorders including depression. Any dissociative disorder has more red flags and symptoms than just memory gaps so you should probably do your own research to learn more about it.