I have received the following explanation of the origin of my name.
My special thanks to Christopher Wilkinson from Canada

If I'm not mistaken, Myrea comes from the Greek root for the same word that in french is Mer, or "the sea," with the feminine singular nominalizer --"ea" added. Woman of the Sea??

One related name I know is Prelea. Prel/ea.
Lots of these names found their way into Irish Celtic and Gaelic areas, probably in the course of the shipping/trade between Scandanavia (Vikings/norsemen), the British Isles, and then down around Gibraltar to the ports of Greece and Italy, Alexandria, etc.

If I had the time to look deep
Through the books of lore
I know I would look first for King Neptune
And find the Sea Queen's name
Think of the Mer, the Myr, and so
The Mermaid is too simple for the name, me thinks it well,
And the trident sea lord with his moon crown glowing
Would be the direction I'd seek the knowing I fear there might be confusion where
The myrtle groves are brought to bear
But the myrtle is the herb of the moon
And the moon is the mistress of the sea
And those wise in the ways of nature
Would know these things well
Do tell,
Whence came thee
And whither thy name and blood
For thence are the secrets of these name
Where the Gaul and the Greek together are bonded in blood
From a time long long before
The Roman Gaulish war
And the peoples of the moors held long the ancient lore
And the names of things from long before
The egret "y" is telling If it's not a new-age spelling
For the mer was the myr and the linn was the lyn
And so go the names of middle English to now,
While the Greek grammar endings were held for the few
With learning, or with blood ties old
To the Mediterranean fold
Your name is probably the sea queen, the moon,
The mistress of the wax and waning of the light of the night
And so I might find told If I had the time
To check these old books of mine.

Christopher Wilkinson
27th December 2001