Guild Wars 2

I think it’s correct that they can be placed in bank….
And that there’s a clear sign that they belong to another character….

But should be written the name of the character the item belong to.

That sounds like a suggestion for ANet to make a change.

Currently, as designed, the game only tells you if an item is soulbound (but does not display to which character it is bound).

I would think it is supposed to be like it is in GW1 were it said who it belonged to.

Yes, it was different (and I agree, better) in GW1. But it’s working as intended in GW2.