The rise of the term Autobot differs with each continuity.
In the Aligned continuity (which is the most similar to the Michael Bay movies), the term Autobot is coined by Orion Pax as a description for the concept of abolishing the caste system that the Cybertronians were living under, not as a description for the race as a whole. "
Autonomous" as in deciding one's fate by themselves.
In the IDW comics continuity the Autobot moniker is given to the corrupt Cybertronian Empire by the galaxy's other races to describe these mechanical beings.
Auto from automatons, because in the other races' eyes the Cybertronians were long lived mechanicals who never changed in any fundamental way
(despite the name Transformers).
When both Optimus Prime and Megatron rise up against the corrupt government, Megatron chose to name his faction with a new name and a new sigil, while Optimus decided to repurpose the term Autobot and derive it from "autonomous" (from the people, by the people) and keep the old sigil.
Which, in essence, displays the philosophical differences between the two leaders.
In the 1984 cartoon continuity the two races were created separately by the Quintessons.
Autobots as consumer grade machines, and the Decepticons as weaponized machines.
So this makes this continuity the only one were the Autobots and Decepticons were never the same race.
In the Marvel comics continuity the Autobots were created by Primus and lived more or less peacefully on Cybertron.
When Megatron started his revolution he decided he needed to differentiate his faction, and so gave them a new name.
As far as I recall, no reasoning is given for the names.
In the Dreamwave comics continuity the two factions arose when Megatron started the civil war.
Those who sided with Megatron named themselves Decepticons, and those who sided with Sentinel Prime and the Council of Ancients named themselves Autobots.
Again no reasoning is given for the names.
scifi.stackexchange.com/users/887/System Down
Originally for toy reasons.
The Autobots were all cars in the original run in 1984, so Automobile-Robots.
Decepticons because they are the bad guys.
Bob Budiansky is crediting with naming the first batch of guys if I remember correctly.
scifi.stackexchange.com/users/1223/Rigas
The Transformers were created by a race called the Quintessons.
They originally created Autobots as general worker consumer bots and Decepticons as military weapons.
The Transformers eventually became sentient and rebelled.
This is far back in their past though.
The more recent factions are more political centric.
It is not uncommon for an Autobot/Decepticon to switch sides.
scifi.stackexchange.com/users/12262/Simon O'Doherty
I think the Japanese naming is an interesting contrast (especially as TF started as a rebrand of two completely separate line of Japanese toys).
The Japanese name for the Autobots is (literally) Seibertron (or Cyberton) -
so Cybertronion is seen as synonymous with the "good guys".
The Decepticons on the other hand are known as Destron (from destroy/destruct) - an obvious anti-faction there.
scifi.stackexchange.com/users/16661/sHtev
Autobots have blue eyes or optics; Decepticons have red.
(At least, that's what I noticed in the 80's cartoon series - apart from their insignias)
Therefore, blue is good, while red is rude
scifi.stackexchange.com/users/59630/Nelson Josef T. Fernandez
The title 'Autobot' is explained to be the short version of 'Autonomous Robotic Organisms'. Wouldn't that mean all Cybertronions are Autobots? Why then do the good "Heroic Bots" lead by Optimus Prime call themselves Autobots while the bad "Evil Bots" lead by Megatron call themselves Decepticons? Aren't they all the same race?
What is the difference between an Autobot and a Decepticon
scifi.stackexchange.com
<transformers>
scifi.stackexchange.com/questions/55374
scifi.stackexchange.com/users/13090/Morgan
In the Marvel comics continuity  the Autobots (car robots) were created by Primus and lived more or less peacefully on Cybertron. Autobots were created as general worker consumer bots and Decepticons were created as military weapons. The Autobots become civilian vehicles and equipment while the Decepticons, for the most part, take the form of military vehicles.
The Autobots become civilian vehicles and equipment while the Decepticons, for the most part, take the form of military vehicles.