Before everyone blows up that rag gheirat Irani and we are the center of the world cheer , let me make couple of points:
1) Many iranian artists (some "legendary ones", in the past, have stolen songs/melodies from neighboring countries/cultures and even far lands of Greece/Latin America..................
2) While there is a good possibility that this lady wanted to capitalize on brand name of gogosh ( Atashin) ( I'm not sure how well known our gogosh is among new generation of Uzbaks), it is note worthy that Gogoosh is actually a nickname.
It has been customary among Turkic cultures to have nick names in addition to your official given name. This also true in Iran and Azarbaijan, at least up to a generation or two ago mostly in smaller azari/Turkish populated areas and villages.
Practically no kid will be called Ibrahim , they were all Ibos...All Fazl-ollah were Fazan.. And many arabic sounding names had their Cuter nick name version..Arabic Names starting with GHAF were almost assured of having a cute partner nickname. Gogoosh, while not very common, was just one of this nicknames picked for both males and females, usually in liue of Ghhodrat khanoom, Ghodrat Ollah, Ghamar, or such........Why? that is another story,
I have personally known 3 kids called Gogoosh, one male ( he always hated it but his parents kept calling him that) , and 2 females. None aspiring to be singers or becoming copy cats of Gogoosh the singer......
Again ,I'm not saying that this lady is absoluetly not capitalizing on our Gogossh fame ( if any), but it is also possible that she had this nick name or liked this nickname growing up in Turkic Culture....
The fact that she is calling herself GogooshA , with Pasvand A distinguishing female, suggest that there may be a male version in her environment and possibility that even males could have been nicknamed gogoosh.
Pasvand of "A" is russian influence distinguishing females from males in Turkic areas that lived under Soviet Union. You will even see that in Azari names ,north of border (O-Tay_).
Before passing strong and emotional judgments, lets get to know each other's culture better and learn not view everything from one particular shade of glass.