The other dinner guests do not do this scriptural exegesis. They don't think, "She must be a prophet. Ergo, he must be a king." Rather, they focus on what seems to them to be the foolish waste. And the contents of the jar were expensive--almost a year's pay.
Jesus reminds them of what they surely already knew--they are going to have many opportunities to use resources in what seems to be the right way--taking care of the poor. After all, the poor are not going away. Circumstances will continue to foster poverty.
Jesus points out to them that what this woman has done in this place on this day is is to prepare his body for burial. Yes, kings were anointed, but also are those persons who are to be buried.
The irony in Mark's version is that Jesus then says that wherever the good news is proclaimed in the whole world, what this woman has done will be told in remembrance of her. Yet, Mark doesn't tell us her name.
Later, in a Passover meal with his closest disciples, Jesus tells them that one of them is going to betray him.
Then he takes bread, blesses it, breaks it, and gives it to them, saying "This is my body." He takes a cup, gives thanks, and gives it to them, saying, "This is my blood of the covenant, which is poured out for many." We continue to remember this supper as disciples continue to gather.
The incident of the anointment of Jesus by a woman is told in all four gospels--and, with variations among them. In Mark's version, she is not named, nor are the objectors. Try not to worry about harmonizing the details. Rather, use them to help understand what particular message that particular gospel writer is trying to get across to us.