The pronunciation of my last name often confuses people who do not speak Russian, especially in North America.
My recommended "Americanized" pronunciation is /tuck-TEY-ef/. So, three syllables: "tuck" as in "to tuck in", "tey" so that it rhymes with "hey", and "ef" as in the name of the letter "F".
For a somewhat closer "Euro" approximation, replace the "ck" in "tuck" with a "hard H," like the "ch" in German "nacht" or the "j" in Spanish "ojo".
The next level up requires mastery of the Russian "soft t", which few languages have and which is usually very hard to learn.
I've discovered that while in the United States and Canada people usually try hard to not mispronounce my name (which in practice usually means going to great length to just avoid saying it at all), in Brazil everyone just goes with a heavily Portuguesified form without worrying much about what the "correct" pronunciation would be. This is actually fine by me, as it makes my life in Brazil quite a bit simpler than in US and Canada.
I was born on the 15th anniversary of Yuri Gagarin's space flight. My parents have always denied that this had anything to do with their choice of name, but there was never a shortage of other people pointing out this association. "Yuri" actually has an extra "y" sound at the end (i.e., "Yuriy"), but this "iy" is very difficult for non-Russian speakers to pronounce, which is why it is normally reduced to just "i".
A Russian name normally has a "middle name", which is derived from the name of the person's father and is called a "patronymic" in English. Mine is "Vladimirovich," referring to my father's name "Vladimir". The patronymic is very important in Russian because the standard polite way of addressing an adult is by a combination of the first name and patronymic. (So, if one wanted to address me politely in Russian, they would say "Yuri Vladimirovich" rather than using a title and my last name.)