The Russian is Достоевский, yes. And the accent falls on the "e", yes. And Е is Russian for "ye" and the non-palatized "eh" sound is spelled Э.

However, how many "y"s are you going to write. Are you going to write Lyenin instead of Lenin? Or perhaps even Lyenyin? After all, both vowels are palatized. Also, how are you going to translate ы and й and и? The first is a non-palatized "i" with a slight w- sound, which sounds as though you're trying to say "oui" but down in your throat. It is usually transliterated as "y". However, the й is a consonantal -y at the end of words and it is frequently transliterated as "y" as well, which leads to some confusion. Then there is the palatized "i", и, which is usually transliterated as "i" but which is palatized.

Thus, if you want to really be correct and consistent, you would spell the name:

Dostoyevskiy

or, if you use a -j to avoid confusing ы and й, you would spell it:

Dostoejevskij

I prefer, however, to spell transliterated Russian with as few letters as possible. This means that I only spell "e" as "ye" if it BEGINS a word, as in:

Yeltsin (rather than Eltsin)

However, even then first names are better of without the "Ye", so I write Elena and Ekaterina instead of Yelena and Yekaterina.

So, to sum up, I transliterate as follows:

1. -iy and -yy always end up being transliterated as -y
2. Russian E never becomes "ye" except at the beginning of a word that is not a given name
3. ы is translated as "y", as is й