The Middle Ages lasted for about a thousand years in most parts of Europe, from about AD 500 to about AD 1500, depending on the particular definition of the Middle Ages.
And Europe is a very big place, about as large as the United states of America, and so at the beginning of the Middle Ages it had a very diverse set of cultures outside of the former and the remaining territories of the Roman Empire. Just as there were hundreds of separate Indian or Native American cultures and societies in the USA before the arrival of Europeans - there are still 573 federally recognized tribal entities in the USA today - there were hundreds or thousands of often tiny tribal groups in most of Europe, the parts which had not been ruled by the Roman Empire, at the beginning of the Middle Ages.
So there were many differing cultural habits about war in different societies at the beginning of the Middle Ages, which tended to more or less merge into a common European way of making war by the end of the Middle Ages and early Modern times.
So it is possible that some warriors in some groups at the beginning of the Middle Ages might have gone into battle wearing nothing. But as a general rule Medieval warriors wore clothing in battle and armor if they could afford it. And the more stratified and less egalitarian a medieval society was, the greater was the difference between how well equipped low ranking and high ranking warriors were.
So I think it would have been pretty obvious who the higher ranking enemies were.
Emperor of the Romans Basil II conquered the First Bulgarian Empire in a series of wars up to 1018. There is a story that one time Bulgarians ambushed a detached force. When word reached Basil, he rode off in a hurry toward the fight with his small staff. When the Bulgarians saw Basil's personal flag and knew he was coming they yelled "The Tsar! the Tsar!" and fled in terror. So obviously the Bulgarians knew the design of a unique flag that marked the presence of Basil and his staff.
And it is quite possible that it was the usual practice for a ruler to have flag of unique design to mark their presence on the battlefield all through the Middle Ages.
Heraldry developed in the 12th century (AD 1101-1200) in western Europe and spread to most regions of Europe by the end of the Middle Ages. A noble, knight, or monarch, or other person with a coat of arms (by the end of the Middle Ages heraldry spread to all social classes including clergy, women, Jews, townspeople and peasants) could use their coat of arms design on their seal, their clothing, their pennon or banner, and their shield to show who they were. So in later Medieval warfare many warriors used their coats of arms in battle, and the more high ranking they were, the more likely they were to have a coat of arms, and to have a coat of arms that even enemy warriors might recognize.
Different uses of heraldry were used on battles in different eras and different places in the Middle Ages, so one cannot be certain that a specific military use of heraldry would be common at a specific time and place. Nor can one be certain that all users of heraldry would use in battle all aspects of heraldry they might use in a tournament or other form of pageantry. The higher ranking someone was the more likely they would be to use all forms of their heraldry on the battlefield.
In my answer here:
I listed all the possible different uses of heraldry on a late Medieval battlefield. And I described how a messenger or attacker looking for a Lord X might identify Lord X in a period when all heraldic military uses were fashionable at the same time:
So if you were looking for Lord X you might notice a group of soldiers wearing his livery colors and copies of his badge, with Lord X's standard flying, and among them someone wearing Lord X's coat of arms (and maybe his horse was wearing Lord X's coat of arms) and holding a shield with Lord X's coat of arms, and wearing Lord X's crest on his helmet, and accompanied by someone carrying a banner with Lord X's coat of arms, and you would begin to suspect that that person could possibly be Lord X.
I have read that at the Battle of Benevento on 26 February 1266 King Manfred of Sicily wore a silver eagle on his helmet which fell off during the battle.
During his campaign in France, Henry V of England wore a gem-encrusted helmet that included the Black Prince's Ruby.2 In the Battle of Agincourt on 25 October 1415, the French Duke of Alençon struck Henry on the head with a battleaxe, and Henry nearly lost both the helmet and his life. The battle was won by Henry's forces and the Black Prince's Ruby was saved. Richard III is supposed to have worn the gemstone in his helmet at the Battle of Bosworth, where he died.
According to contemporary English accounts, Henry fought hand to hand. Upon hearing that his youngest brother Humphrey, Duke of Gloucester had been wounded in the groin, Henry took his household guard and stood over his brother, in the front rank of the fighting, until Humphrey could be dragged to safety. The king received an axe blow to the head, which knocked off a piece of the crown that formed part of his helmet.
King Richard III of England was killed attacking Henry Tudor, the future King Henry VII, at the Battle of Bosworth Field, August 22, 1485:
After the battle, the royal crown, which Richard had worn into the fray, was picked out of a bush and placed on Henry’s head.
Of course Henry VII's official coronation, with the official coronation crown, The Crown of Saint Edward, didn't happen until 30 October 1485, in Westminster Abbey.
So sometimes kings would wear crowns on their helmets in battles.
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Have many links to sources of information on medieval heraldry and to other questions on similar topics.