Basically, COMPUTER is not an abbreviated word or acronym, so there is no full form of it. However, computer lovers and users have generated many acronyms and full forms of it. Few are:
C = Commonly
O = Operating
M = Machine
P = Purposely
U = Used for
T = Trade, Training
E = Education &
R = Research
The other is-
C = Common
O = Operated
M = Machine
P = Personally
U = Used for
T = Trade
E = Education &
R = Research
The other is-
C = Common
O = Oriented
M = Machine
P = Particularly
U = United and used under
T = Technical and
E = Educational
R = Research.
Another is in a different style:
Com + Pu + Ter
Complete Purpose Terminal
or
Co + M + Pu + Ter
Complete Multi Purpose Terminal
Remember, these are just terms to describe what a computer is.

O = Operating
M = Machine
P = Purposely
U = Used for
T = Trade, Training
E = Education &
R = Research
The other is-
C = Common
O = Operated
M = Machine
P = Personally
U = Used for
T = Trade
E = Education &
R = Research
The other is-
C = Common
O = Oriented
M = Machine
P = Particularly
U = United and used under
T = Technical and
E = Educational
R = Research.
Another is in a different style:
Com + Pu + Ter
Complete Purpose Terminal
or
Co + M + Pu + Ter
Complete Multi Purpose Terminal
Remember, these are just terms to describe what a computer is.
The term 'computer' comes from the Latin word 'COMPUTARE', which means 'to calculate' or 'to count.' Originally, it referred to people who performed mathematical calculations. Later, the term was applied to machines that could perform such calculations.
These kinds of expansions are just BACKRONYMS