I'll try with an answer as well, trying to be Solomonic between @Tyler Durden and @fdb.
TL;DR: Yes, it's a coincidence.
As @Peter Diehr lists from Behind the Name entry for Diokles the meaning is given as
Given Name DIOKLES
USAGE: Ancient Greek
OTHER SCRIPTS: Διοκλης (Ancient Greek)
Meaning & History Means "glory of Zeus" from Greek Διος (Dios) meaning "of ZEUS" and κλεος (kleos) meaning "glory".
Διος is the genitive.
The etymology of Zeus is given in the Online Etymology Dictionary as
supreme god of the ancient Greeks and master of the others, 1706, from
Greek, from PIE *dewos- "god" (cognates: Latin deus "god," Old Persian
daiva- "demon, evil god," Old Church Slavonic deivai, Sanskrit deva-),
from root *dyeu- "to gleam, to shine;" also the root of words for
"sky" and "day" (see diurnal). The god-sense is originally "shining,"
but "whether as originally sun-god or as lightener" is not now clear.
κλεος makes an appearance in a number of other words, such as the latinised Cleon, and also the name of the muse Clio
[the] muse of history, muse who sings of glorious actions
and also, Hercules, in its Greek form Heracles, itself derived from Hera (wife of Zeus) and kleon, giving us Glory of Hera.
Wikipedia gives the -anus ending as adoptive cognomen, meaning a suffix to indicate Diocletian would have been adopted (not unusual in the Empire). For those allergic to citations from Wikipedia, here also Roman Nomenclature
Adoption: An adult son of a family which already had a male heir could
be adopted into a family which did not have a surviving son. The
adopted man took all three names of his adoptive father and usually
added the adjectival form of his own clan name, formed by adding the
suffix -anus) to his own nomen. Thus, when Gaius Octavius Thurinus was
adopted by his great-uncle, Julius Caesar, his formal name became
Gaius Julius Caesar Octavianus. At the time, those who addressed or
referred to him respectfully would do so as "Caesar" or "Gaius
Caesar"; those who wished to be denigrating or disrespectful would use
his adoptive, "Octavianus." Modern historians usually call him
Octavian until he officially added the honorific Augustus (“the
revered one”) to his name in 27 BCE
According to De Imperatoribus Romanis Diocletians full name was
Gaius Aurelius Valerius Diocletianus