I also wonder, what my name means and wether our familiy might be noble. I found hints to that on: familienkunde.at/Adel_Polen_Namensindex_H.htm
Your Austrian source contains this entry: HANOW, HANOWSKI vom WAPPEN JASIENCZYK, which actually means that the families Hanow and Hanowski (alongside some other 130 families in Poland) were entitled to use Jasieńczyk coat of arms (alternative: Jasienice, Jasiona, Klucz).http://en.wikipedia.org/wiki/Jasie%C5%84czyk_coat_of_arms
You need to realize that only in the Polish heraldic tradition, as opposed to the West European traditions, the coats of arms have their own names and they are rarely associated with one family only. One reason for it was a so-called adoption process to the coat of arms, existing in Poland already in the fourteenth century, and particularly frequently used in the fifteenth century. It was based on the official "adoption" of a person (being ennobled) by someone from the old nobility to their coat of arms. Often the adoptee was given a variation of the original coat of arms.
There is a historically known fact of the collective act of adoption of Lithunian gentry and Ruthenian boyars to the crests of leading Polish magnates after the Union of Horodło, 1413. Since the adoption to crest posed the potential for abuse, adoptions for fee, purchases of the gentry status and uncontrolled growth of gentry each adoption required approval of Sejm (Parliament), beginning with the mid XVI c.
Your surname, alongside many other surnames beginning in "Han", is either derived from female name Hanna (Anna) or from German male name Han, an abbreviation from Johann, Johannes (= Jan). In Poland, during middle ages, the given name Han was equivalent to the name Jan. Consequently, in many cases, the surname Hanowski could be a re-spelled name Janowski.
The Hannowsky surname is probably just a variation on Hanowski; I would not take much notice here regarding the spelling difference. For example, one of the "Han-like" villages in old Poland, is (still existing) Hanowo, gmina (municipality) Grudziądz, district Grudziądz, Kuiavian-Pomeranian voivodship. It was once spelled Hannowo in German.
Hanowski is just more popular than Hannowsky. In Germany, there are 147 phone book entries with the name Hanowski (estimated 392 people), but only 14 entries for Hannowsky (estimated 37 persons).
In Poland, there are 100 registered people of the name Hanowski, and none of Hannowsky. Just few of them are in Krosno Odrzańskie county; which includes town of Gubin.
There is no easy way to prove whether or not your ancestry was of noble origin, or if they were just peasants or tradesman born in or around various villages with the prefix "Han" or "Jan". You would have to go back generation, after generation - repeating exactly the same process, through which many of the Polish gentry had to go in 19th c. to prove to Prussian, Russian and Austrian partitioning powers that they were indeed of documented Polish gentry, worthy of some privileges, such as not being subject to forceful conscription to tsarist armies.
Nevertheless, the noble Hanowski clans were spread all over Polish-Lithuanian Commonwealth. Some used to live in Warmia:
Here is what father Franciszek Bałuta wrote in a baptism book in 1947:
From the old times when Warmia belonged to Polish Republic - from 1466 to 1772, 300 hundred years or about nine generations - the traces of noble and folk surnames still remain. To the first group of names, found in the baptism book, belong the following old gentry names: Błoński (former Jabłoński), Czodrowski (former Szczodrowski), Koskowski, Szarnowski (former Czarnowski), Ossowski, Pogorzelski, Wilkowski, £ęgowski (now Langowski) Dębski (now Demski, Tempski) Jankowski, Muchowski, Lubowiedzki (now Lubowitzki), Witkowski, Grabowski, Grodzki (now Grotzki), Hanowski (=Janowski), Barczewski, Makowski, et multa alia his similia.
Other "Han" surnames belonged to nobility of Wołyń (Wolhynia), Podole (Podolia) and Kiev lands: Han, Handerf, Hankiewicz, Hanneman, Hanowski
, Hanzak, Hańkowski, Hański.
Ornatowski's index of Polish nobility lists the following names, which seem to be derived from Han (h. is an abbreviation from "herb", a coat of arms):
Hanaszewski h. Gąska; Hancewicz h. Pomian; Hanczewicz h. Gozdawa; Handa h. Doliwa; Hanel h. Odrowąż; Hanicki h. Korczak; Haniewicz h. Nowina; Haniewski h. Pomian; Hankiewicz h. Awdaniec; Hankowski h. Korczak; Hanow, Hanowski h. Jasieńczyk
; Hannowiecki h. Junosza; Hanusiewicz, Hanusowicz h. Korczak;
Hanuszewicz h. Radwan; Hański h. Gozdawa, Korczak
And there are many villages in Poland starting in "Han". The good help here would be an old book in Polish, available for free as e-book: Słownik Geograficzny Królestwa Polskiego i innych krajów słowiańskich, Volume 3, By Filip Sulimierski, Bronisław Chlebowski, Władysław Walewski, Warszawa 1882.
(A geographic dictionary of Polish Kingdom and other Slavic countries). Find the name, such as Hanowo, get it in Wikipedia, then locate it on google maps, and then follow historical details. Nowadays, many local websites present their history in English as well.