Jóhanna frá Örk, mærin frá Hleðringum

1) Lorraine
The original name of Lothar's kingdom was regnum quondam Lotharii or Lotharii regnum ("kingdom [once] Lothair's") and its inhabitants Lotharii (from Lotharius), Lotharienses (from Lothariensis), or Lotharingi (which gives the modern German Lothringen, which is the name of the province). The latter term, formed with the Germanic suffix -ing, indicating ancestral or familial relationships, gave rise to the Latin term Lotharingia in the tenth century.
The name Lothar is mentioned as Lóthar in Icelandic dictionaries, but should be HLÖÐAR(R). It has NOT the same origin as Icelandic Hlöðver and the German-Icelandic variant Lúðvík. I really have to emphasize this because I had discussions about this in the past with some Icelanders and they kept on insisting ad nauseam that 'Hlöðver' and 'Lothar' were the same or so phoneticly close that they can be equalized. They can NOT. If we are to built a correct Icelandic name for the region we must start from a correct Icelandic equivalent of the German personal name. Hlöðver and its cognate Lúðvík are derived from ChlodoWICH (Old High German Hludwíg, Hluotwíg (meaning 'famous warrior', Old Scandinavian rune inscriptions: *hlauðuuigar (see Íslensk orðsifjabók), while the original form of 'Lothar', on the other hand, is 'chlodoCHAR', the ending of which means 'army', corresponding with the '-ar' (in this case the ending in Icelandic masculine personal names. So the Icelandic version should HLÖÐAR(R) (ending from -herji) not Hlöðver (from vígar). There's a very slight difference between these three forms, but this difference should be made. The name of the region is simply the plural form of the '-ing' derivation: Hleðringar (German: Lothringen) from Hlöðar(r) (Lothar)
So the Icelandic version of Joan of Arc's epiteth "Maid of Lorraine" translates as "Mærin frá Hleðringum".

2) Orleans:
The emperor Aurelian renaming the old city Aurelianum, which evolved into Orléans. The Icelandic version of the Latin personal name Aurelianus is 'Árelján' (Icelandic Árel- in Árelíus + -ján in Kristján (compare: -ianus/-ján, AurelIANUS/ ChristIANUS)). The name of the city becomes Áreljánsborg (New Orleans = Nýja-Áreljánsborg)
The Icelandiv version of Joan of Arc's epiteth of 'Maid of Orleans' becomes 'Mærin frá Áreljánsborg'

3) Guðbrynmey
The eccentric, strictly Icelandic construction Guðbrynmey is an epiteth built like a personal name. If someone in Icelandic wants to name his daughter exclusively after 'Joan of Arc', merely calling her 'Jóhanna' wouldn't suffice. This is where constructions like Guðbrynmey could come into play. The following constructions are possible:

1) Guðbrynmey with or without a second personal name (Guðmey in itself could also apply to the holy virigin, Saint Bernadette from Lourdes and probably many other female saints, while Brynmey, without the Guð- prefix as a reference marker of the christian faith could refer to "Pallas (means 'virgin') Athena", the armoured warrior godess in Greek mythology.)
2) The combinations Jóhanna Guðmey, Jóhanna Brynmey or Helga Brynmey are also possible in case people find "Guðbrynmey" too long.