Whatever its adaptation, it would have to be elected. That would be up to the people of Scotland. And, as you describe, that incarnation would need to be different to what we have now. The base of support for the SNP is for independence so, by definition, that support would transfer to other parties. But I would ask, WHY would they keep the name? It would be defunct.
Obviously the main platform for SNP is to obtain independence but there is no reason why the party itself (like others in the past all over the world have done) can't adapt its raison d'etre to be running the country after independence is gained, this whole idea of it not existing because its objective has been achieved is flawed.
And that is the concern as most politicians are much the same, irrespective of the party they represent.
ETA Would this new party be any better or worse, that's the big question that nobody can answer with any authority.