My undertanding is that, yes, present-day amnesia is required by the DSM to qualify for DID. BUT I'm not sure that the amnesia needs to be ABOUT present-day. The DSM says...
"Recurrent gaps in the recall of everyday events, important personal information, and/or traumatic events that are inconsistent with ordinary forgetting."

That last point is always confusing, because what if you have amnesia of trauma from the past?

However, the DSM is not the only guide for diagnosis - there is also the ICD, which is being revised, I believe.

I have heard that the ICD is possibly going to combine the OSDD-1 & DID diagnoses. OSDD-1 has two categories: 1b and 1a. OSDD-1b is basically DID without amnesia and OSDD-1a includes amnesia, but the alters are not complex/"fully formed" or whatever you'd like to call it.

All this is to say...
as much as I know it FEELS important, because validity, the truth is...the criteria for these diagnoses are just a bunch of old white dudes sitting in a room coming up with definitions. I know I, personally, struggle a lot with parts who are very very tied up in diagnoses and being "official"...but, the truth is, they freak out whether the answer is "yes, your DID is valid" or "no, you do not have DID." There is no answer that satisfies them, and there never will be.

As much as this is totally pot calling kettle black, my best advice is to try to sit with the ambiguity: maybe you have DID, maybe you don't. But one thing is for sure -- you exist, you have a way of experiencing & interacting with the world and with yourself, and that is something worth exploring -- a label shouldn't change any of that.