Gothenburg was founded a century after the end of the Kalmar Union.
But! There were at least three predecessors in the prior centuries. It was a pretty exposed position, so it got burnt down sometimes.
So...
If a KU king wants to create a new city to be capital of the Union, this location would be fairly logical and telling the merchants in what town/city was nearby to relocate to a chosen site was something that was done OTL.
The name would likely not be Gothenburg though. Maybe something that refers to the king or to the Union? Maybe rename the Union after this new city?