There have been kings for thousands of years, across continents and different situations but I'll try to give a general answer. I'm assuming what you are imagining is a king of a stable country (rather a kingly contender in a civil war) of a dynasty that has had time to bed in.

Even absolute rulers were not free to do whatever they wished. At least, not without consequences that they need to consider when making a decision. Even a Son of Heaven of a long-lived dynasty which was the biggest power in the region couldn't always, for example, choose his Empress but have to accept the chosen one of the court. A ruler lives among structures, among cultural attitudes, among situations and people, all these rulers may be able to shape and influence but they couldn't always escape it.

A strong ruler could take a decision that... might be unpopular if they were determined to push something through, against the advice of officials and amidst protest, but there would be consequences. That could simply be burning a lot of political and/or diplomatic capital or helping destroy a dynasty.

So your the King of AskHistoriania, a noble and proud country but you wish to rise further, to be an Emperor. To reflect your heavenly majesty and authority, to elevate yourself to the deserved highest ranks. So you summon your closest advisers to see what barriers there might be...

How well does this go down abroad?

Other Emperors may not take so well the idea that you consider themselves on their level and consider this a challenge to their position that needs to be dealt with before others decide they also could be Emperors. Other King's might be rather offended at you putting yourselves above them.

You probably have allies. This could range to all sorts of dynamics, for example, superior powers acting as a protector and support but this elevation of yours is challenging that power-dynamic. Mutual allies of trade and cooperation of sorts who might feel their nose put of joint or become worried about your reliability given the step you have just taken. You could have junior allies or vassal powers who might be questioning how safe it is to be aligned with you or seeing a chance to break out from under your influence.

You may also have hostile states even if they aren't outright enemies. Ones who may see this as a chance to isolate you from your allies, take advantage of any troubles in your lands and perhaps even justify a war. Particularly if your elevation is a challenge to their authority.

You will need to either smooth the way beforehand so they aren't caught by surprise and perhaps be persuaded of benefits in supporting your claim to Emperor. Or be prepared for angered allies who you may have to hope to decide the benefits of the alliance still outweigh this or even losing them, ending up alienated abroad. Have an army ready prepared to defend your claim for rival powers or to bring rebelling vassal powers back under your sway by force.

For something like becoming Queen or giving yourself an insulting title, you might become a joke. Being seen as weak may make your allies uneasy and your opponents perhaps eye up a chance to gobble your lands, your ability to assert your influence abroad if you are a laughing stock is unlikely to be high.

What about your loyal subjects?

This might also not go down well with them. Is this a leader getting too big for his boots and placing himself in too high esteem? Do they fear the idea is dangerous and could bring downfall due to others may react, does this reflect badly on your mindset? Are there connotations within the society that might be averse to change of title or Emperors?

If more something like the insulting title, slapping the face of your nation or mocking them via "King of Dogs" is... unlikely to go down well. Changing to the title of another gender title may challenge their view of the world, the natural order of which your own powerful families rely on and might raise questions about who of which spouse fills the defined, by tradition, roles in the court and the administration.

So what could your peons do? Protest in private and if it leaks out that one of your most senior ministers, of great standing, is against it then that will be embarrassing. Or go public via resignations, words in court, memorials or whatever the society of that time has to argue this is inappropriate. All this will hit your reputation and that of your court, having the service of great men under you adds prestige and authority to your crown and losing them tarnishes it, it can raise doubts about you.

Your leading families may well take actions to show their displeasure though what they could do would reflect the systems in place and the power dynamics: refuse to help in future military expeditions with their private soldiers, they may be a little less keen for public service but show their disdain by refusing office, not rushing to pay their taxes. These aren't insurmountable but they will require finding other methods to fill the ranks, to fill the coffers and raise troops and when you might be facing other problems. Is it worth taking the step?

Worse, a King has protection via a sense of legitimacy of lineage, history and heaven but it isn't automatic protection. Dynasties end, kings die in war or via murder. There may well be other rivals (of your blood or a past dynasty) around with claims to the throne who may be sensing an opportunity to gather support at home or abroad. Or an ambitious leading member of the gentry who will be painting themselves as a more modest, conventional, sensible figure who would, if backed by the other noble lords of the realm, bring the realm back from the brink of disaster. Possibly not as King themselves (initially) but the man in charge

You have the resources of the state in theory and likely at least some in practice, that is if all your soldiers aren't tied up elsewhere or deserting you. But their own lands and connections (plus any helpful reinforcements from abroad) will allow them to raise soldiers needed to potentially destroy you. Be it via death, control or abdication (with potential death to follow).

This isn't the say you couldn't pull off the change with enough preparation (diplomatic work, persuading your vassals, building a case for the legitimacy of your ascension) and in the right circumstances, elevating your status and that of your descendants to come, increasing the prestige of your dynasty. But the challenges before you could be difficult and would need to be taken into account before you made such a move.

In terms of why someone else naming you mattered, it could strengthen the claim to legitimacy. If it wasn't yourself claiming to be Emperor via bloody sword and ambition, there are plenty of such men about, but instead being pushed into it or declared by another power then who could call you a power-hungry ambitious tyrant with no sense of propriety? You are simply obeying the calls of others to take on this terrible and unexpected burden. How willingly they gave you the title is a minor detail, just as long as it looks willingly given to you.

It could be the past dynasty Emperor abdicating to yours and so passing on the heavenly mantle, directly connecting your rule with the legitimacy of the dynasty that came before. Or your loyal subjects "persuading" you to take the step despite your modest and oh so humble objections. Or outside my sphere of expertise a figure of religious authority declaring you to be chosen by the authorities of a God/Heaven, showing to your subjects and to those abroad that you have authority from higher than mere mortals.

It looks good for the history books, for your descendants and your own authority if it looks that was not instigated by you but an authority put on your shoulders by the people, by a heavenly authority that puts your claim above other men of power. It hopefully makes it just a little bit harder (though far from impossible) for another power, domestic or abroad, to make a claim against your rightful place if you can point to the support of a authority beyond your own.