They must have known they were getting kings by another name. Were they scared of the power, or just OK with the seizing of power, just son long as the taboo of the name wasn't crossed?
This question opens up so many doors for so many kinds of answers, and so I will deal mainly with how and why Octavian-Augustus managed to become an Emperor by any other name.
The years just before and following his successes are known as the principate (27 BC - AD 284), characterised by "first citizens" maintaining sole power whilst simultaneously keeping up the illusion that Rome was still a republic.
After the outcry and general dislike of Caesar's consul-for-life blunder, Octavian knew that, following his victory over Anthony and Cleopatra, he was in a position of supreme power in the republic. However, wanting to appease both the aristocrats and the plebs following a long and bloody war, he incrementally increased his influence whilst assuring that he would restore Rome to its republican roots.
By promoting and sponsoring certain people he maintained control of many careers within both the army and senate, ensuring that his ideas would always carry weight.
Slowly but surely he had a number of political titles given to him with the clause of having them "for life" - at this point in time (around 25-27 B.C.) it was his wealth, his army and his driving personality holding up the Roman empire, not the senate. He was still, however, the Princeps - the first citizen - not an emperor.
What must be understood is that Octavian was everywhere. He made sure that every building he built had his name and face, that he attended public gatherings and pandered to everyone's concerns. He performed acts that a legally elected magistrate or official would need to do, but as a private citizen without office.
In 22 B.C. he also sought out, tried successfully and executed men who had previously attempted to bring him to trial for overruling senatorial orders not to attack Thrace - based on charges that they were attempting to kill him. Some time after this he was also named "Father of the Country" and pontifex maximus, the most important position in Roman religion. By this point Octavian Augustus was basically running his own side government alongside the senate that actually had all the real power.
When he died it was equally important to make sure he wasn't appointing an heir per se to take over. As such he made sure those he earmarked were well known to the Roman people and their qualities would mean they deserved the title of first citizen. The senate and people were all too ready to swear Tiberius (famous as a prosecutor, lawmaker and general) in as successor and the game continued, with the senate's power growing weaker and the imperial cult growing stronger until it became more about having a "strong leader" than a free senate.
I apologise if my (very brief) summary doesn't answer the question as deeply as you would like. I'm sure there are some excellent historians here that can go into more detail.
My sources:
Possible further reading: