First please bear a little grammatical digression: Some words beginning with a vowel in Greece have a 'rough breathing'. These words in English always begin with an h or an s. For example 'yper' becomes 'hyper' or 'super' in English, as 'omogenos' becomes 'homogenous', the Goddess Estia becomes
Hestia etc.
The Sun, 'Elios' becomes '
Helios' in English. So, to return to your question, if a Greek
Elias were to be related with the sun, his name would be definitely be spelled with an rough breathing (Helias) as with
Helios. Alas, most Eliases in contemporary Greece have no rough breathing. However I have seen some Eliases using a rough breathing, to claim an etymological link with the Sun
To see if there were any Heliases in ancient Greece, I checked with Lexicon of Greek Personal Names
http://www.lgpn.ox.ac.uk/lgpn1.html. Indeed, there are records of the following ancient Greek 'Helias' ¡V related names:
Helias (f)
Helios (m)
Helion (m)
Heliodoros (m)
So it is not a pure coincidence :)
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