The word "computer" isn't an acronym or abbreviation, so technically, there isn't a "full form" of the word...
However, you might be interested to learn a bit about how we ended up with the term 'computer'.
The full form of computer
As mentioned, the word computer doesn't stand for anything.
However, the word originates from the idea of 'computing' or calculating. Rather than machines, the first computers were technically humans!
In account, finance and the military - the term 'computer' was used to describe someone whose job it was to compute complex sums or mathematical problems.
Everything from firing artillery through to managing financial books required a 'human computer' at hand back then.
So, before the invention of the computer as an electronic device, the term computer existed to describe what we'd probably refer to today as "human calculator"!