I am wondering if there is a short form(s) of Italian name Adriano?
Googled but could not find anything. Thanks in advance.
The only abbreviation I'm aware of is "Adri", like Josh61 states. It can be used for the less frequent female name "Adriana" as well.
Note that, like many Italian name abbreviations ending with the "i" sound, it can both be written locally ending with an "i", or with an "y" to give it an international tone. Apart of being some sort of Anglicism, I'm positive many people see abbreviations ending with a "y" more suited for female names.
In your case, also if no official rule is defined (I'm only giving my view on what's more informally used based on my experience), you could abbreviate Adriano in "Adri" and Adriana in "Adry", although the sound is the same.
Also note that near Rome and central Italy (Lazio region), but in the south as well (Campania and in particular Naples come to mind), almost every name that has an "a" (even if it sounds strange in case the "a" is in the first syllable) is abbreviated putting an accent on it and cutting the name there. So, Adriano becomes "Adrià", Pasquale is shortened to "Pasquà" and Giovanni to "Giovà". Please note that, apart of being a rather regionalized use, such abbreviations is more common when speaking directly to the interested person (more commonly, when calling out loud to catch his/her attention, maybe when seeing him by chance and greeting him).
I agree with @Josh61 on "Adri" and I would like to add something about its pronounciation. Due to the effort in articulating the cluster /d/ + /r/, the voiced alveolar fricative may sound doubled and the /a/ shorter (/addri/). Just to make myself understood, this also happens in some regional dialects with the word "libro" which becomes /libbro/.