Exactly this is possible with Civ 3 (C3C expansion) and the C3X mod: The names, images and titles of leaders can change in each of the four eras of Civ 3. The era change for each civ is fixed, so there is no problem in the identification of the different civs.
Per example this is the civilopedia entry for the civ Egypt in the Civ 3 mod CCM 3, showing the different names of the 4 leaders in the four eras of Civ3 when starting a game and even accessable during the complete game (for Egypt only the names of the leaders and their titles are changing during the 4 eras of the game, for other civs even the names of the civs can change):
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Here you can see the names of several leaders and civs, changing during the 4 eras of the game (Egypt is in the southern part of that animation):
Here you can see the text file for the configuration of the different leader names and titles in CCM 3:
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Here you can see the configuration of the names of a civ in different eras of a game in CCM 3 when it was thought that this is helpful (with that method all 31 civs in Civ 3 could be handled):
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Flintlock and his C3X mod in my eyes here has created a masterpiece, that could also be very helpful for Civ 7.
In the current CCM 3 the different leaders only have the function of "cosmetics" and no direct influence on the game. This will change with the new version "CCR" that is in works and tries to give the different leaders a small own personality by added building functions to every single leader, what now is possible in Civ 3, as now the limit of 256 buildings in Civ 3 has fallen.