In response to your editing: in this case, you simply throw an exception. It just happens in a catch block. Instead of using potentially confusing terminology such as βtransformationβ (which, I think, implies a mutation, not something new), I suggest you just say what you are doing explicitly.
You "wrap" the caught exception to another. Another term for it is "exception chain"
Notice that the repeated exception is different from the other, because you are not creating a new exception, just catch it to make some entries (or something else) and then throw them away again. To demonstrate:
try { operation(); } catch (SomeException se) { throw se; }
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