So, I know about Soulstones and Frostmourne, but can a potent enchant or any other mean imbue an object, such as a weapon, to a person deeply spiritually (As if they were one and the same etc.)?
Unlikely.
Edit: Actually, upon pondering about it, Shaman are capable of having a significant spiritual connection with another item which makes them capable of sacrificing it in order to rebirth themselves upon death. Although, it has to be very significant to them.
I see. For I was thinking if Death Knights could have a soul bond with their runeblade.
In that case? Nope.
Third Generation Runeblades channel their runic power, they have nothing to do with souls.