That is the common rule to localize the pronunciation of your name when introducing to foreigners in their language. It applies to any language I think.
When introducing myself to Americans, I say: "My name is Constantine" with the first syllable stressed, American "o" in "Con" and American "t"'s.
If you pronounce "Меня зовут Robert" to Russians, you make their life harder:
1) they would most likely have difficulties with hearing it correctly unless they are fluent in English;
2) they would definitely have problems with repeating your name.
"Роберт" is a well-known name in Russia, we also have people with this name. But the American pronunication can make it even unrecognizable to the Russian ear: the American "o" sounds almost like Russian "а", and the American retroflex "er" sound is something competely alien and unpronounceable to Russians. If not to say that many Russians hear the American alveolar aspirated "t" as "ч".
As for the "Mc" part, it is just a well-known tradition to Cyrillize it as "Мак".
Don't worryIf you had to introduce yourself to a Japanese, you would have to say "Watashi-no namae-wa Robaato desu". And in the case of Chinese, it would be something like "Wo jiao Luo-Bei".