In the eras when full plate armor was worn bare, without a cloth cover, to show off the metal, it was decorated in various ways. There could be patterns of contrasting polished and rough unpolished metal, patterns of different metals on the surface, patters of gilded and ungilded metals, patterns of fluted and unfluted smooth metal, etc., etc.
And all the photos of such highly decorated armor that I have seen have the patterns seem too small-scale, intricate, and fussy to be much good at identification.
Identification was much easier in the eras when knights wore garments like surcoats and tabards displaying their coats of arms over their armor.
I think that sometimes the surcoat would be the color of the field of the coat of arms and have many copies of the charge in the coat of arms scattered over the surface. And sometimes a surcoat, and always a tabard, would have one iteration or copy of the coat of arms on the front side and one on the back side and one on each sleeve.
An ordinary warrior who had a coat of arms, up to a knight bachelor, would have a pennon attached to his lance with his coat of arms on the flag, while a higher ranking warrior, a knight banneret or higher, would have a banner with his coat of arms, and the banner would usually be carried by a banner bearer.
So a knight banneret or higher lord would have a personal flag, and the garments he wore over his armor would have the same pattern as his personal flag. So it would be like wearing copies of his personal flag as his clothing.
But there's more! In some eras a warrior would carry a shield, and shields were almost always decorated with patterns, and so when heraldry was invented any warrior who had a coat of arms would put it on his shield.
But that's not all! A knight could have his horse wear horse cloths that had several iterations of his coat of arms.
In some eras knight wore crests on their helmets, sometimes two dimensional cut outs, sometimes three dimensional models. The designs of crests were sometimes identical to the coat of arms, sometimes based on it but a bit different, and sometimes totally different from the coat of arms.
for even more icing on the cake, in some eras various lords had badges, emblems different from their coats of arms, but sometimes identical to their crests, which they put on their personal possessions and also had their retainers wear small copies of. Warriors and servants of a lord would sometimes wear civilian costumes and military uniforms in the livery colors of the lord, which might be the colors of his coat or arms or badge or different colors.
So if you were looking for Lord X you might notice a group of soldiers wearing his livery colors and copies of his badge, 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.
If the President of the United States went into battle wearing the coat of arms of the USA which is "Argent, six pales gules, a chief azure" (white with six thin vertical red stripes, and across the top a blue bar) he would wear a surcoat with "Argent, six pales gules, a chief azure" in front and in the back, and one on each sleeve, and carry a shield with "Argent, six pales gules, a chief azure", and wear a crest over his helmet of "a glory with 13 mullets on blue field" (A circular cloud with rays of light surrounding a blue field with 13 stars).
His horse would wear trappings with "Argent, six pales gules, a chief azure", and he would be accompanied by a banner bearer with a banner of "Argent, six pales gules, a chief azure".
The coat of arms of the Count of Habsburg was "Or, a lion rampant gules, crowned azure" (a yellow field with a red lion rearing up wearing a blue crown) and the coat of arms of the Duke of Austria was "Gules, a fess argent" (red with a white horizontal band in the center). The coat of arms of the count of Nassau was "Azure, billety or, a lion rampant or" (a blue field strewn with yellow rectangles, a yellow lion rearing up).
The King of the Romans was the person elected Emperor of the Romans but not yet crowned emperor in Rome by the Pope. The coat of arms of the King of the Romans was "Or, an eagle displayed sable" (a yellow field with a black eagle with wings spread out, having only one head).
Adolf, Count of Nassau, was elected King of the Romans in 1292, but the Electors declared him deposed on 23 June 1298 and elected Albert, Count of Habsburg and Duke of Austria, as King of the Romans. Albert and Adolf fought at the Battle of Gollheim on 2 July 1298. The angry Adolf sought out Albert and you can be sure Adolf made an effort to learn beforehand what the coats of arms of Habsburg, Austria, and any other fiefs claimed by Albert looked like if he didn't already know such famous coats of arms. Albert unhorsed Adolf and dismounted to finish Adolf off.
A poem written centuries later claims that both Adolf and Albert wore the coat of arms of the king of the Romans on their surcoats, yellow strewn with black one headed eagles. That is logical since the king of the Romans was theoretically the rightful ruler of everywhere and so was the highest possible position, and one which both Adolf and Albert claimed.
Since the coat of arms of the king of the Romans was one single-headed eagle, it would have been quite possible that both Adolf and Albert actually wore surcoats with one eagle on the front, one on the back, and one on each sleeve. Producers of historical movies should note that if Adolf and Albert both wore surcoats semi (strewn with an arbitrary number) of eagles they would not have looked identical, having be made by different makers for different clients. Thus they would have different numbers of eagles of different sizes and with different design details, and someone could tell the difference when Adolf and Albert were facing each other.
In some battles the lord or king would wear uncovered armor or a plain surcoat and one or more brave knights would volunteer to wear surcoats with the lord's coat of arms to attract enemy attacks. I think that I read of one battle where the king in disguise survived and about a dozen knights who wore his coat of arms were killed.
Knights, lords, and kings sometimes wore civilian robes emblazoned with their coats of arms, which would be highly desirable from a visual standpoint in any fictional medieval fantasy world.
As far as I know, the only way to make bare metal armor have as distinctive a pattern as a coat of arms would be to paint the coat of arms in full color on the metal of the armor.
And it seems to me that wearing surcoats or tabards with the coat of arms over the armor would be just as good as armor painted with the coat of arms, especially if the character also wears similar garments with the coat of arms in civilian settings when he isn't wearing any armor.