Dear Mike C
Of course the word "dexter" is Latin, but it derives from the Greek word "dexiteros" (m) - "dexitera" (f)!
I am familiar with the explanation that etymonline.com gives.
However: The first historically proven use of the "PIE" ("Paleo Indo-European") base *dek- or *dex- as a prefix with the meaning of "right", is found in the Greek Linear B scripts (1500-1200 BCE):
dek-a-sa-to, dek-o-me, (words)
DEX-EYS, DEX-I-FOS (names) etc.
and not in any other "Indo-European" or Latin language. With simple words, that lead us to the scientific conclusion that the elements
*dek-, *dex- derives from Mycenaean Greek, until a finding of another inscription older than Linear B scripts changes that fact.
("Documents in Mycenaean Greek, Three Hundred Selected Tablets From Knossos, Pylos and Mycenae, With Commentary and Vocabularies". Michael Ventris and John Chadwick, Cambridge University Press, 1956.
"Corpus of Mycenaean Inscriptions of Knossos", Volumes 1-4. John Chadwick et al, Cambridge University Press.)
As for etymonline.com, (or any other etymology work written or online as far I know), although it does a good job, to my humble opinion it needs to be updated with Linear B vocabulary, a most important tool for the science of etymology, after it was deciphered by M. Ventris and J. Chadwick in 1953.
Obviously, 'If parents DO give the name intending it to mean "skillful", then it is much more likely they have the Latin word in mind.', since officially it was through the Romans that the Germanic tribes (Anglo-Saxons etc.) got in contact with the ancient Greek civilization. (Although unofficially the first contacts between Western Europeans and Greeks took place in much earlier times, i.e. Pytheas and older:http://en.wikipedia.org/wiki/Pytheashttp://www.ahepafamily.org/d5/pytheas.html
PS: LGPN (http://www.lgpn.ox.ac.uk
) covers 91 names with the prefix Dex-, including two Dexters.
"Until the day that an ancient inscription will be found with the name "Alexandrovski" (or "Alexandrev" or "Alexandrov") written on it instead of "Alexander", true Macedonia and true Macedonians will remain Greek, as they always were."