They may not have had photographs, but they did have paintings and sculptures, and these were widely dispersed. However, it is possible that many of these were not particularly well-executed. We have extant a letter from the tutor Fronto to his pupil Marcus Aurelius laughing about this.

You know how in all the money-changer's bureaus, booths, book-stalls, eaves, porches, windows, anywhere and everywhere there are likenesses of you exposed to view, badly enough painted most of them to be sure, and modelled or carved in a plain, not to say sorry, style of art, yet at the same time your likeness, however much a caricature, never when I go out meets my eyes without making me part my lips for a smile and dream of you.

Also, we have the interesting culture of guest-friendship. Aristocratic standing was recognised internationally and they could move freely: there was extensive mobility at the highest social standing.

Guest-friendship entailed a network of international friends and acquaintances of similar social standing. We have many 'introduction letters,' which exist, where a friend of a friend is introduced to someone in a new city where he is travelling.

So let's say I'm an aristocrat in one Greek city-state and want to visit another city. A friend of mine knows someone in that city-state and so writes to him, introducing me. He tells of our relationship, my family, when I was arriving, and so on. So it would be rare for someone of high standing to suddenly show up. He would be expected, and if he was not people would be curious and perhaps suspicious. At the very least a travelling aristocrat would carry letters of introduction with him.

Once I arrived at my destination, it would be expected that I give my new host expensive gifts of movable wealth, like gold plates or other valuable items. My host would reciprocate and give me something. These gifts might be specifically inscribed. Many of these which we have found in tombs are engraved with banquet scenes, because one of the main features of this guest-friendship was feasts and drinking parties to welcome the new guest. In this way he would be known to even more people in the community. So if anyone was trying to be an impostor they would have to be quite rich.

Now that I was known to many aristocrats in this new city I could write my own letters of introduction. Maybe one of them wants to visit my city, or a friend in my hometown wants to follow in my footsteps and visit the new city. They would ask me to write letters of introduction and the international network would be strengthened and expanded.

Sources: Loeb Fronto I and Cornell, The Beginnings of Rome