Egalitarianism vs Individualism
Slavery seems to be the only basis written to call for the name change, most likely because of the slavery penalty/bonus from either ethos. But if you've been following, the topic of slavery becomes less emphasized when it comes to affecting the empire's policy-making options via collectivism vs individualism.
Egalitarianism has very blurry line (yet very simply put, it is 'equality'), so it is often hard to tell which egalitarian idea you are emphasizing about when you say "egalitarian". Egalitarianism also has impure meaning, if the OP wishes to put it as universally as he did. One can identify some aspects of collectivism in egalitarianism. Its ideas, mainly economic, is very close cousin to (or is) socialist ideals. And it's quite clear that socialism has many ideas sprung from collectivist stance. Most importantly, egalitarianism does not contribute to government forms, but influences the structure of the government - how it is or will be made up, its constitutions, power distribution among leaders and subjects..etc. This is mainly because egalitarianism is form of many principles and doctrines that make up the view of equality; whereas individualism is purely a moral stance. This gives egalitarianism a hard time when trying to distinguish which government type it belongs to. This also means that the view of egalitarianism can also change in the hands of different societies or culture groups. But in our world, it is embedded within the "western democratic societies" and has become the norm/gold standard when it comes to political and social egalitarian thinking. Notable example of western egalitarian thought would be how most democratic countries are set up; checks and balances for US government; and how everyone is able to elect their own leaders.
A democratic state says to its citizens:
"A man is able to vote for a leader in a democratic country (individualism), therefore all of its citizens have the RIGHT to vote (egalitarianism)."
Egalitarianism by itself has no basis to eliminate slavery or have democratic government forms. Individualism however, is invalid in autocratic countries in terms of politics, while egalitarianism can be valid (even meager but equal rights is considered egalitarian).
If we are talking about class, there would be upper class, middle class, and lower class. Slave class would be separate entity because slavery, throughout history, is permanent with very few special exceptions. It is something that no one wants to be and strips away individual rights. Individualists would certainly steer away from it, but egalitarianism has nothing to do with steering away from slavery. The only reason egalitarian thought can be applied to abolish slavery is the fact that not everyone can have equal rights as slaves, but is otherwise ALLOWED if the state deems that all its citizens be slaves, because the highest possible standard would be the slave class. In this case, the egalitarian thought would have no influence from individualism's "realization of self-worth" whatsoever.
"All are equal (to a set point)" vs "individual's worth" are very different things. No matter which philosophy you look at it from, no humans in an individualist society would naturally want to become a slave. Therefore, if you apply the principles of egalitarianism that derive from individualist thought, you are obliged to eliminate the slave class from the society. Notable society where egalitarianism is heavily conflicted with individualism would be the United States and many western countries. And I say conflicted because:
"I'm a worthy human being. I shouldn't be a slave, because I don't want to be" is a individualist's thought, whereas "I shouldn't be a slave, because everyone else are not" is egalitarian (in a world where western standard of equality is what most desire, which means no slaves). If you put them together, egalitarianism is bound to be surpassed by individualism. This is why meaning of equality is ever changing in countries like the US, to make it compatible to individualism. People would want to decide for themselves how worthy they are, rather than be acknowledged as an equal. This means individualism naturally eliminates slave class, whereas egalitarianism relies on individualist idea it's basing the "equal standard" on, in order to eliminate slave class. Individualism can also be associated with capitalism or free market economy, which is why there are multiple classes of people rather than one, even if the government policies are based upon egalitarian thinking (US).
Individualism does contribute to government forms, in this case: Indirect, direct, and moral democracy. Individualism does not contribute to make-up of the government, unlike egalitarianism. However, it can affect the hierarchical structure and how one takes power, WITHIN the structure of the government. It makes sense for a individualist society would favor democracies, because every individuals would have their own wants.
In an individualist society, slaves won't exist - not simply because the society wouldn't allow it, but also because the society is awake in self-realization in a sense. And the society values individuals. Therefore, they wouldn't tolerate slavery in the first place. With egalitarianism, an individual can be considered a mere cog in a machine by the state, and given same rights as the other cogs, especially if the state deems such rights to be the best possible rights for all.
The answer is clear that, individualism is more plausible for democracies and eliminating slavery. Egalitarianism is very weak in this regard. It has history with "human rights and equality", but the basis for the "equality" and the standard of "rights" is continuously being changed by major political and social groups in the world. And it is being changed heavily based on individualist ideas. So to conclude, egalitarianism can be seen as a pursuit (in human world) for individualists. If a gay community grows into a larger voice, and wants same marriage rights as the traditional family (individualist wants), the state will give them such rights (egalitarian) or won't. If the feminist activists want whatever rights they want these days, the state will give them the rights or won't.
