The current tag Artoria Pendragon (Caster) (Fate) is, frankly, blatantly incorrect, if not misleading. Below, I will explain in spoiler tags why that is the case (FGO Lostbelt nr. 6 spoilers), and why the tag should simply be Artoria Caster (Fate).
Artoria Caster is actually not 'our' Artoria Pendragon. She's really a wholly unique entity spawned from the English Lostbelt, the Child of Prophecy who is meant to bring salvation to Faerie Britain. In truth, she has absolutely zero relation to PHH Artoria, and I feel that information should be properly respected.
Likewise, I would suggest that Lostbelt Morgan be appropriately tagged: something like Morgan (Lostbelt) (Fate). She, too, is not a Lostbelt equivalent of her PHH counterpart; her real identity is Tonelico, the original Child of Prophecy. There's a whole shitload of time travel stuff going on that's currently really tough to explain, but suffice it to say that Lostbelt Morgan is very much a distinct entity compared to PHH Morgan; because she's not really Morgan.
I hope the outline here is clear enough, but I'll try to answer any questions if something's unclear. I'm simply trying to convey what FGO proper has established.
Thank you for reading, and have a good day.