If we look at the names assigned to her on a meta level, we know that she was named after a well known mythical figure:
14. This player is female and decides that her character will also be female. Inspired by the name of Morgan le Fay from Arthurian legends, the player decides that the name of Morgan Ironwolf would be a good name for a fighter.
And I'm not the only one thinking that the Ironwolf might've been inspired by the Howard Chaykin comic character.
But what if we go beyond that surface level of naming and weave a bit more backstory into Morgan Ironwolf's past -- especially if we plan on making her a higher level NPC that the players run into?
According to Wikipedia, the name Morgan can mean "magnanimous", or by turns (based on the translation you wish to believe) "Great Queen" or "Phantom Queen" -- though both these names are derived assuming that you agree that Morgan is taken from the name Morrigan.
Morgan le Fay certainly does spring to mind, and we know that this mythical figure was originally fey or a fairy (and later tales made her a mortal spellcaster or enchantress). Interestingly, Morgan le Fay's first name is theorized to be drawn from the creatures known as the Morgens -- water spirits that drown men.
As a surname, Morgan is also affiliated with the sea, meaning "sea chief" or "sea defender".
In my mind, Morgan Ironwolf's background would imply some lineage of royalty or perhaps nobility of a sort (perhaps derived from a line of defenders on a border, or perhaps the daughter of a war chief from an island kingdom). That faint touch of magic -- water magic, sea magic, fey magic -- and the character's chosen profession of fighter and adventurer suggests that this one may have been named for some ties (suspected) to magic.
Clearly, however, she has turned her back on that path.
And perhaps this is a clue to that as well. Her surname (possibly an epithet) can be broken up into Iron and Wolf for inspiration.
Wolves are rife in myth and legends. Aside from the wolves that are central to the founding of cities and empires, and the numerous magical wolves and monsters tied to pantheons, wolves are also sometimes associated to witches and witchcraft.
With the presence of iron, a material traditionally positioned as a counter to magic and fey creatures, it could be argued that she is of a lineage or destiny that may:
a) found a city through the might of arms;
b) become a terror through near-magical skill with weaponry;
c) forge a path that unites her mystical path with the steel-based weaponry of the dawning era.
All this may depend on an individual's campaign, but certainly the seeds are there for using Morgan Ironwolf as a interesting plot hook for your D&D campaign.