Seems to me that the name should be "Alfordians" or "Alfordian sympathizer."
"Loyalist" is a term generally used for factions within a country or organization. Outside of a revolution or civil conflict, it doesn't have much usefulness (I mean, you could say "Alfordian Loyalist," but that's about the only way I could see that word being used in this context, and even there it doesn't make much sense outside of an area of Lahren that was once ruled by Alford).
"Monarchist" only really works in the context of whatever political entity the character is living in, and if there is a dispute over where there should be a monarchy, or if one should be restored. If a you have a character in Lahren who is a monarchist, this would refer to a monarch of Lahren, not Alford.
"Allegiant" is a fancy word, but it also doesn't work on its own - it's the same as just saying "ally." It would have to be "Alfordian Allegiant," or something like that.
In history, when people are claiming an allegiance outside of their nationality, it tends to involve the name of a political movement ("Communist," "Fascist," "Nazi," Abolitionist," "Democrat," "Liberal," "Imperialist," "Anarchist," etc.). So, what may be the best approach to solve this dilemma is to name the political movement first ("Friends of Alford," etc.), and then that will give you the term that will best serve your story.
