One source of much confusion is the connection - or lack thereof - between the Irish goddess the Morrigan and the Welsh Arthurian figure Morgen le Fay*. I've been meaning to write about this for a while but have hesitated because I am admittedly weak on the Welsh end of things and didn't want to do a disservice to the subject. However I've had several people ask me recently about what connection there might be between these two, so I feel like this needs to be said.
The short answer - historically there is no connection between the Morrigan and Morgen le Fay.
The Morrigan - The Morrigan is an Irish goddess with complex associations to battle, war, death, prophecy, sovereignty, magic, incitement, and victory. Her name in older forms of Irish was pronounced roughly 'MORE-rih-guhn' and later forms 'MORE-ree-uhn' and meant either great queen or phantom queen, depending what etymology one favors. We have a wide selection of mythology and folklore featuring her and it's clear that when she shows up she's an active force in whatever she's doing.
The Morrigan has two sisters, Badb and Macha, who she appears with in some myths usually performing battle magic; in the Tain Bo Cuailgne she also appears with Nemain and Be Neit for the same purpose. The Morrigan in later mythology would come to be associated with night terrors and specters, viewed as demonic because she could not easily be turned into a meek saint.
Morgen le Fay - Morgen le Fay is a character first found in Arthurian stories, specifically the 12th century works of Geoffrey of Monmouth, where her name was initially spelled Morgen le Fay. It is worth noting that this spelling is significant because while both Morgan and Morgen are men's names (also worth noting) they are pronounced differently - Morgan evolved into the modern Welsh Morcant while Morgen became Morien (Jones, 1997). In the 12th century Morgen would have been pronounced, roughly, 'Mor-YEN' (Jones, 1997). The name Morgen is generally believed to mean 'sea born'.
Geoffrey was collecting local stories from Wales and publishing them in France and while he certainly didn't invent Morgen for his Viti Merlini there is no way to know for certain how much or little he shaped the character as he preserved her. Which in fairness is true for all of the Arthurian characters he wrote about. That aside however Geoffrey's Morgen was a priestess, one of nine sisters connected to Avalon. In the 15th century Morgen would be renamed Morgan by Thomas Malory and recast as King Arthur's scheming half-sister who was set against both Arthur and his wife Guinevere.
The Evidence - One of the main arguments connecting the names is that they sound the same to modern English speakers, but I hope it's clear here that in Irish and Welsh the two names sound very different. They also have different meanings and that is significant. Another argument that favors their being the same deity is that they are both connected to magic, but while one may argue that both do indeed practice enchantment the nature of the magic they practice seems to be vitally different and outside of that single similarity the rest of their associations are very different. Morgen is connected to healing and, perhaps, to guiding the dead or dying to Avalon/the Otherworld; the Morrigan is associated with death and battle but nothing in her mythology relates her to healing or to a role as a psychopomp. People also argue that their stories have similar themes, but this is clearly not so: the Morrigan is married to the Dagda and may or may not try to seduce Cu Chulainn in one story while Morgen in various stories is married, is adulterous, and even tricks her own brother into conceiving a son with her; the Morrigan incites battles by directly encouraging people to rise up and fight while Morgen in some of her stories sows discord in more subtle ways; the Morrigan's main location is a cave, Uaimh na gCat, while Morgen's is an island on a lake, Avalon. These are only a few examples just to illustrate the very different natures of the two beings.
The Morrigan and Morgen le Fay are often associated with each other in modern paganism, perhaps because they are both perceived as powerful and potentially dangerous women who have gotten a bad reputation that they may not deserve. Both certainly were vilified and demonized over time as stories evolved, the Morrigan going from a goddess to a night specter and Morgen from a priestess of Avalon to an incestuous and usurping sister of the king. I certainly understand why people see associations between the two, although for myself I'd be more likely to picture them sharing stories at the bar over shots together than to believe they are the same being or energy.
I cannot say whether or not Morgen is a deity or ever was a deity, nor do I deny that someone does answer when people call on Morgen le Fay today. What I can say is that there's no evidence that the Morrigan and Morgen le Fay share any roots or that historically the two have any connection to each other.
*I am aware that in modern terms her name is often given now as Morgan la Fey however I am choosing to go with the older original spelling used by the first person to write her name down.
MacKillop, J., (2006) Dictionary of Celtic Mythology
Jones, H., (1997) Concerning the Names Morgan, Morgana, Morgaine, Muirghein, Morrigan and the Like. Retrieved from https://medievalscotland.org/problem/names/morgan.shtml
Gray, E., (1983) Cath Maige Tuired
Dunn, J., (1914) Tain Bo Cualgne
Morgan la Fay (2018) The Camelot Project; University of Rochester. Retrieved from http://www.kingarthursknights.com/others/morganlefay.asp