This is my "official" name used in all the documents, bank accounts, visas etc. There exists a long-standing official Russian tradition (which goes back to the XIX century) to spell Russian names in the French way. When the Soviet authorities deliver a foreign passport, they do not ask your opinion on how your proper name should be spelled.
This spelling is used in my publications. Why don't I change it to the French style now, if I live in France? - I just don't want to appear in two different forms in bibliographies (including bibliographies to my own papers!). Let it be my pen-name. And the name "Zvonkine" is from now on reserved to my son Dimitri Zvonkine.
(I would say that my problem is a minor one, being compared with others'. A friend of mine has all his publications signed by Shubin. And in his passport it is written ... Choubine!)
Michel Mendès France proposed to adopt, as my official name, the spelling "Zvonkin(e)". It would probably be a unique case in the history when the parentheses are used as part of the name. It might even deserve an entry in the Guinness Book. But I did not dare to take the risk.
(Added in proof. My colleague Anne Dicky has informed me that her great-grandfather, for some complicated biographical reasons, during certain period of his life had a family name with parentheses: "Dicky (Perediry)". Therefore, I would be neither the first such case nor the only one. No point in trying.)
Sasha is to Alexandre what Bill is to William, Bob to Robert, etc. This form is used in communication with friends, colleagues and relatives.
The word "Kalmanovich" means the only thing: that my father's first name was Kalman. In the same way, my son is Dimitri Alexandrovich.
(The name of Ilich Ramírez Sánchez is just a linguistic anecdote. He is called in this way in honor of Vladimir Ilyich Lenin. But "Ilyich" means "a son of Ilya". To give such a name to one's child would mean to say "in fact, he is not my child: he is a son of Ilya".)
The version "Alexander Zvonkine" is slightly incoherent, because it is a mixture of French and English style.
To say "Salut Sacha!" is perfectly OK. But to write "Monsieur le professeur Sacha Zvonkine" looks bizarre. In this case "Alexandre Zvonkine" is preferable.
Even more bizarre is "Sacha Kalmanovitch"; it would certainly make Russians laugh.
I will not dwell here on the questions why my daughter is Zvonkina (and not Zvonkine); why she is Alexandrovna (and not Alexnadrovich), and so on. Neither will I discuss the declination of the proper names in Russian (many difficult points even for the native speakers).