Viro doesn't look anything like Estonian Eesti (or English Estonia) because it originates from the name of the historic county Virumaa (modern-day Ida-Virumaa and Lääne-Virumaa). So I guess it's similar to the way many languages call the Netherlands some variant of Holland, where the name of a county became used for the name of the country.
Nobody's sure exactly where the Estonian Viru comes from but it may ultimately from the Proto-Indo-European word wiHrós "man" and so would be related to English virile ("manly") and werewolf ("man-wolf").
Arguably, "lovely" can also be a synonym of "beautiful" https://en.wiktionary.org/wiki/lovely
But you're right, kaunis=beautiful is a better fit, I just hate typing "beautiful", it usually takes me 3 attempts before I manage to put the -eau- in the right order :D Blame the ranskalaiset for such spelling.