"Locutus" is basically Latin for "He Who Has Spoken." Picard was assimilated to be a spokesman for the Collective, and his name was based on that. (Well, actually it means more like "he who was talking just now." But that's close enough.)
"Logos" is a Greek term meaning a word, a concept, a principle, an explanation -- it's a very complex term. In the Biblical "In the Beginning was the Word," "the Word" is only a rough translation of Logos
, the term used in the original Gospel. It means both the expression of a concept and the concept itself, both a word and its meaning -- "And the Word became flesh." Dave could explain better, but I'd guess that the Queen called her Logos because she was "the one we have waited for" -- the being that would give the Borg not only a new voice but new meaning.
Why are these names in Latin and Greek? Because it's Star Trek
and aliens always seem to speak Latin or Greek.
Or maybe because the Queen was coining these terms for human listeners, or maybe because the Borg descend from a human origin anyway.
That's one great thing about the Borg origin revealed here. It never made sense to me that a race of alien cyborgs would call themselves a name that's clearly derived from the English word "cyborg." But if they started out human, it makes a lot more sense.