In the battle of Carrhae Crassus's son, Publius, was killed in a disastrous cavalry charge and his head dangled in front of the rest of the Roman army on the end of a Parthian spear which had a very bad effect on their morale. How would people have been able to recognize that this was actually Publius considering the distance and possible damage the head suffered? Would soldiers even in an army of tens of thousands have been familiar with their commanders appearances such that they could recognize them easily? Was there anything stopping the enemy from finding some random corpse and pretending it was a crucial commander they were showing off as having been killed to sow confusion and loss of heart?
With respect to the Carrhae example, Crassus' seven-legion force ~(32,000 men) might perfectly well be expected to contain some thousands of men who knew Publius Crassus by sight. In the first place, he was sort of a celebrity, because he had previously served under Caesar in Gaul, and had gotten favorable mentions in Caesar's published account of the war, which was very widely read. He also held certain political offices in Rome, in particular that of augur, which, although short on formal legal power, was a very public sort of a job, although he didn't hold it long.
Then, too, a Roman camp was a pretty busy place, and compactly built. For an army of seven legions, it would have amount to a small mobile city surrounded by a palisade wall, which was sometimes built every night upon arrival and dismantled for transportation whenever the army decided to move on. A soldier going about his daily routine might easily see Publius ride by in the company of his father the supreme commander, wearing fancy clothing (more on that later), and ask his neighbor "who's that guy?" And one of the soldiers nearby would probably be able to tell him "Oh, that's Publius, Old Man Crassus' boy. He conquered Aquitania or something, wherever that is. Some guy was reading from Caesar's book in the pub one night and I heard all about it." Caesar was said to know the name of every single centurion in his army, and although neither Crassus is said to have risen to that level, there would have been enough person-to-person contact for lots of people to know what most of their high command looked like.
Roman officers also wanted their troops to be able to identify them during the battle. They would often wear a robe called a paludamentum, which was often in a bright (and, at that time, expensive) color like crimson or purple. One contemporary commentator actually gives this as the etymology of the word as coming from "palam" or "plainly visible," and explains that the whole point of wearing the thing was to make you stand out.
So although you're right that not exactly every single soldier in Crassus' army would have known Publius by sight, given that large numbers of men were standing there in a hollow square, shoulder to shoulder, if any one of them were to blurt out "holy shit, that's Publius Crassus!" lots of people would hear him and most would understand what that meant, and rumors would quickly spread.