In the delightful film "Young Frankenstein", Marty Feldman ("Igor") insists to Gene Wilder ("Dr. Frankenstein") that his name be pronounced the way he wants, to sound like "Eye-Gore". But anyone who knows their Tolstoy realizes that real Russians pronounce it "Ee-Gore". And in the final analysis, the people who own the names should determine how they are pronounced.
So it's a good sign that Americans working the US/Russian space deal have gradually been getting their Russian pronunciations right. People rarely say "MURR" for Mir ("Meer") any more, although they still tend to capitalize it all ("MIR") as if it were an acronym and not simply a proper noun.
And many Russian space names are fairly straightforward, with a common sense American-eared "first guess" being fairly close. That works fine for names such as Progress, or Raduga, or Zenit, or Kvant, Kristall, Priroda, and Spektr -- even though the stressed syllable doesn't always come out quite right.
But "Soyuz" is a problem. The "y" is deceptive. In the standard orthography for transliteration from cyrillic into latin latters, the "yu" stands for a specific Russian letter, so it can't be split. This makes the syllables So-Yuz, not Soy-Uz.
There's a lot of leeway in pronouncing each syllable. "So" with a long "o" seems straightforward, but since the spoken stress is on the second syllable, Russians tend to slur the unstressed "o" into a neutral "ah". "Yuz" has a long "u", in "ooze", not a short "u", as in Buzz. Also, in speaking, voiced final consonants tend to become unvoiced (the "z" shifts to more like an "s"), but this isn't too important.
Try: for "Soyuz", say "sah-YOOZ", or if you're more ambitious, "sah-YOOSS". But please, drop the "Soy" Sauce, and don't make Soyuz rhyme with Coy Fuzz.
This troublesome "y" always used to confuse Jules Bergman, the ABC-TV space reporter during the Space Race. Whenever he talked about the Soviet launch site at Tyuratam, he made it four syllables: TIE-YOUR-A-TAM. It was supposed to be T'YOU-Rah-TAM, only three syllables. And since the Soviets deceptively called it "Baikonur" decades ago, people have gotten used to using the false name anyway.
Why does it matter? Proper pronunciation of other people's names is always a sign of respect and it will be appreciated. It's worth the effort.
Another example: generations of English-speakers pronounce Vladimir and Boris with stress on the first syllable. Russians stress them on the second syllable. It may not seem like a big difference but try shifting stress on some American multi-syllabic first name and see how it grates on our ears.
Even though Sergey Krikalev is a very diplomatic and easy-going man, and has probably gotten used to Americans mispronouncing his name, try getting it more authentic. His name ends in a variant of "e" that sometimes has an umlaut over it and is pronounced "yoh" or "yaw", and is always the stressed syllable. So it's not KREE-kall-ev, it's closer to kri-kal-YOFF (remember how voiced consonents become unvoiced at the ends of words). The same goes for STS-71 passenger Anatoliy Solovev (sah-lav-YOFF), Moscow MCC ("TsUP" with a long "u") deputy Vladimir Solovev (vla-DEEM-er sah-lav-YOFF), Soviet space program founder Sergey Korolev (kah-rahl-YOFF), and even ex-premier Nikita Khrushchev (khroosch-YOFF).
"Energia" has a hard "g", to rhyme with Carmen Ghia. And they've changed the initials from "NPO" to "RKK" when they "privatized in mid-1994. Meanwhile, that e-umlaut letter also appears in the middle syllable of RSC Energiya's director, Yuri Semenov (so the proper pronunciation is "Simm-YAWN-off"), and also with chief RKK-E interpretor Boris (ba-REESS) Artemov (art-YAW-moff).
"Buran" has a flat "a", is in "don", not a wide whiney "a" as in "ran" or "Anne". The "u" is long ("boor"), not short ("burr"). And stress the second syllable. As the ancient Romans said, "De mortuis nil nisi bonum" (look it up).
>From old "Space Race" history, there's the "Voskhod", often mispronounced (and sometimes even misspelled) as VOSH-kod. Stress the second syllable and say it "vahss-KH'OTE", to rhyme with "Vostok" (vahss-TOKE). And going WAY back, the "u" in "sputnik" is long, as in "spook", not short, as in "sputter".
The rocket and the communications satellite called "Molniya" are pronounced "MOLE-nee-ya", not "mole-N'EYE-a" with a long "i" in a stressed second syllable.
The Russians call their cosmonaut training town Zvyozdniy Gorodok, or "Starry Town". Back in ASTP days it came to be called "Star City", a somewhat too overblown term for its municipal and celestial status, but the misnomer has stuck. It can be referred to simply as "Zvyozdniy" (pronounced "Z'V'YOZ-nee"), or "ZG" -- or you probably can go with the common, unambiguous usage and stick with Star City, since it's so widespread there's probably no stamping it out.
And please, also, there's no second "R" in Gagarin (no more Gargarin, please!).
Again, why bother to try to get these little things right? Getting them right marks you as somebody who takes the trouble to understand other people and other cultures, and it places you among the real "cognoscenti" (pronounced, of course, cone-yah-SHEN-tee") of Russia and its space program. Getting it wrong might suggest the opposite, I would humbly suggest. Take your choice.