Wavecom docs are often bad, but not that bad! Unless they really messed-up between v3.03 (I have here) and v3.10 (you have?)
The adl_atResponse_t type is described in the ADL User Guide for Open-AT v3.03 on page 24 in the description of the callback function.
As Jan says, the StrData element of the structure contains the unsolicited response.
Maybe that’s what confused you:
What do they mean by the “name” of the response?
It is the repsonse - not just its name!
I think it must’ve lost something in the translation from the original French…
Anyhow, StrData will contain the unsolicited response, as a string, exactly as if you had typed the command manually - so see the AT Commands manual for further details of the content of the string.