i started imagining the political and possibly religious intrigue involved. you know in most kingdoms the royal family is somewhat distant from the nobility. like sure the people loyal to the prince or his family would "want you dead" simple enough but what about the nobles who were plotting usurping the throne to begin with. you possibly threw a wrench in their plans or even worse the more sinister ones, seeing that you are now wanted by a kingdom, may seek to send you an olive branch to pull you to their side to use you for further plans. they know you have no problem killing their enemy regardless of status. think about it most assassins would demand an outrageous sum for that sort of thing and you're out there doing it for free. a good scumbag noble would never let that slip by.
that could technically be seen as a reprecussion, because if, like you said your own kingdom is already sending people after you, and now a whole other kingdom wants you dead, ...pardon, as i havent read your story, but unless your character is some kinda op mega badass, you're probably, possibly going to have to consider accepting their help, which is most definitely not a position you want to be in. same applies if this prince was competing for the crown with a sibling. that sibling, if not outright wanting you dead, is probably not going to stop trying to draw you to their side
having to change identities is probably a repercussion.
not being able to sit still (i just saw the part where you said the mc is basically a wanderer now so ill x that one off)
having the people you care about harassed, demonized, or at worse attacked and imprisoned and tortured to find your whereabouts. or in the religious context they'd probably declare your entire family and anybody close to you as heretics of some sort. this further links into being refused or ostracized by businesses or anything you'd need other people for out of fear for their own safety.
there's a weird one you rarely see in stories but tends to happen sometimes, where, if that prince had any rivals or enemies, they might be the hot-headed type where like.. now that their rival is dead, you become the next target of their unreasonable, unchecked aggression.
if that prince was engaged to a royal of another country seeking to tie the two kingdoms with peace treaties, you probably just destroyed said treaty. while its not a direct repercussion, being single handedly responsible for sending two countries back into war would probably get you hated by a 3rd, previously unrelated country.
idk if this story is a high-fantasy isekai type but if that prince had any sort of blessing or stigmata from that worlds god(s) you most likely just obtained a curse of some sort. or at very least put on some deity-level hitlist.
tl;dr - in any case, just about everything i thought of basically boiled down to "being wanted" still.. just from different angles
(lol in the time it took me to type this up, the previous 2 ppls response basically said most of what i had to say
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