Why is it Medvyedev and not just Medvedev? In Bulgarian to get that pronunciation, you’d have to spell it медвьедев, not Медведев .
Okay, after I wrote that sentence, I typed Медведев into my Google toolbar to make sure it really is spelled in Cyrillic the way I thought it was (and it is) and you know how the Google toolbar pops up an auto-complete list of things other people have googled? The very first thing after Медведев is Медведев - Еврей. I clicked on that out of curiosity, but after a skimming a couple of the articles, I remembered that I don’t speak Russian and I have no idea what they’re going on about. Is Dimitri Medvedev Jewish, or is there some rumor that he is? One of the top articles has the word “sluhi” (I don’t feel like switching back to Cyrillic, sorry) in the title, which I expect means “rumor”, but I can’t decipher any more of it.
I’m only casually familiar with Russian, but the forward facing “e” is usually pronounced as “yeh.” The backward facing “e” is the one that’s pronounced as “eh.” In unstressed syllables and after certain letters, the pronunciations change. Lemme look up the rules. Here’s one page. Read under “notes” to see various pronunciations of “e,” depending on placement.
Closer – here’s a transliteration of his name given in the International Phonetic Alphabet (IPA) used by phoneticians and linguists (from Medvedev’s wiki page), with “Medvedev” in red:
Those little superscript j’s you see in the IPA transileration indicate palatlized consonants, and to English speakers, normally sound like they’ve got little “y-glides” after them. Well, that “dʲ” will actually sound a lot like English “j” in “jiffy” … kind of what palataliztion does to “d”.
EDIT: also at the wikipedia link, right at the very top is a sound file that pronounces his name in Russian.
The letter written E/e in Cyrillic is a palatalized vowel, pronounced “yeh” in isolation, and with a y-ish sound attached to the previous consonant. The vowel with an “eh” sound is somewhat less common (though still fairly common), and looks like the right half of a circle with a horizontal diameter crossbar: Э/э. All ten Russian vowels come in these pairs: A/Я, E/Э, Ы/И, O/ё*, У/Ю. (* Palatalized O does not occur initially.) It’s not a “power palatalization”; the tongue glides past a ‘y’ position as it moves from consonant to vowel, as in Tuesday. Compare “beautiful” and “booty-full” for a good English parallel.
The “soft marker” that looks like a small b is rarely used, I believe only after consonants that otherwise would not palatalize even with a soft vowel following.
And, as Bordelond notes, a fair approximation of the native Russian effect with /tj/ and /dj/ can be achieved with /ch/ and /dzh/=J respectively.
Something else to know about Russian for this purpose is that unstressed vowels following palatalized consonants are pronounced differently than they are when stressed – in the case of /e/, it is pronounced (as you can see from bordelond’s IPA) as *. So the vowels in his name are pronounced, roughly, as [Midvyedif].
Bulgarian consonants don’t have phonemic palatalization, so it’s tripping you up for the Russian pronunciation.
Polycarp, the “soft sign” or мягкий знак before a vowel indicates an underlying iot. In word-final position, it indicates that the final consonant is palatalized. (There are also some contexts where it has a purely grammatical function, but never mind those.) Also, note that in Russian, it is the consonants that are palatalized, but orthography indicates palatalization via either the following vowel, or the soft sign if no vowel follows.
Finally, the word for “hedgehog” does have word-initial ë (ëж), which represents underlying iot plus o.