There are two symbols of sovereignty that were historically crucial for any serious claimant to authority. One is called, in Arabic, the khutbah, which is the communal sermon preached at the mosque every Friday. In pre-modern times, when there was no internet or even a newspaper and a person might conceivably not know who was in charge unless somebody better informed told them, khatibs (preachers) were expected to mention the sovereign’s name at the beginning of their Friday sermon. If the local sovereign was vassal to a more powerful sovereign, the khatib would mention both names in the sermon. If you were the ruler of a particular area and some khatib in a village in your territory started dedicating his Friday sermon to somebody else, that represented a major challenge to your authority and required a response.
The second symbol of sovereignty was the sikkah, or the right to print money. Again to understand the importance here you have to put yourself in the position of somebody living at a time when information didn’t travel fast. If you happened to live in a city or a town controlled by a relatively powerful regional lord, then you very likely knew who that lord was, but you might not know who your lord’s lord was. If you lived in a smaller village with less contact to the outside world, you might not even know who the local ruler was. And really, why would it matter? You’re a peasant, probably a farmer but maybe a craftsman, and you’ve got enough to worry about making sure your family is fed and you can pay the tax collector when he comes by. Did it matter for whom he was collecting taxes? Maybe on some abstract ethnic or religious level it mattered, but guess what? Even if it did matter to you, there was almost nothing you could do about it anyway.
Now imagine you’re the emperor rather than a peasant. How do you know what’s happening in all the cities and towns of your empire? There’s no telephone, not even any telegraph, certainly no electronic communications. You’ve got a bunch of local lords and officials running things, many (even most) of whom might have held the same job for the last emperor (or worse, last dynasty), and virtually all of whom would love to figure out some kind of angle to make some extra money or enhance their personal prestige, at your expense if necessary. You need proof that these people were loyal to you, and it better be regular and public so you could feel reasonably sure that if any of them tried any funny business you’d hear about it. And you’d want to make sure that the people living under them knew, at the very least, who you were.
The khubtah is one way to help solve this problem, by having a trusted authority figure remind everybody in a particular community once a week that you’re the boss. Not only does this keep your name out there among the public, but it’s fairly easy to have agents monitor those Friday sermons and let you know if somebody suddenly began preaching in a different sovereign’s name. The khutbah is frequently mentioned in Islamic history when there’s a rebellion or a change in allegiance.
As important as the khutbah was, the sikkah was at least equally as important because it provided a chance for the ruler to communicate directly with his or her subjects. The first Islamic coins to be minted were literally copies of Roman and Persian coins already circulating in the Near East. This in itself was a statement that the new empire was not here to disrupt the commercial order. When you mint money the first thing you have to do is make sure it looks like what people know to be money, or else you risk nobody using the new currency.
It wasn’t until the reign of the Caliph Abd al-Malik, in the late 7th century, when the caliphate began to strike brand new coinage. The text on Abd al-Malik’s coinage (“God the one, God the eternal, He did not beget and was not begotten”) suggests that this was probably part of a larger project to separate Islam and Christianity over the issue of Jesus’s divinity (Abd al-Malik also constructed the Dome of the Rock in Jerusalem and covered the walls with similar “did not beget/was not begotten” writing, so there’s a common theme at work here). Most Islamic coinage was engraved with words rather than figures, but those words generally conveyed the name and ancestry of the ruler as well as Islamic slogans and then something that would express that ruler’s ideology (maybe the names of the first three caliphs for a Sunni ruler and the names of the line of imams for a Shiʿa one, though a surprising number of Sunni monarchs also liked to cite the imams on their coins).
It’s easy to see why coinage was such an important symbol of authority. Like the Friday sermon, coins will reach just about everybody, and even better than the Friday sermon, the message they convey doesn’t have to go through a potentially unreliable intermediary. To be fair, the degree to which people living in a pre-literate society could read these coins, which if you ask anybody who studies numismatics are hard enough for a literate person to decipher, is debatable, but most people probably knew enough reading to make out the ideological bits (the names of the caliphs and/or imams, for example, or the Islamic slogans), so that even if they couldn’t read the ruler’s name they’d still know that he was a good Muslim.