Air line colors
 

Is it mandatory for airline to paint their aircraft in its colors scheme

If you see how many that do not, I guess the answer is a definite no. The only thing it needs to show is its registration (tail number as our American cousins refer to it). Are you really an A330 pilot?

To be fair, when did aircraft livery ever come up during license or type training? Registration/tail number, yes, but not livery.

Nope. There is no requirement that an airline has its aircraft in a specific or distinct livery (colour scheme). Airlines routinely have specialty schemes or lease aircraft from other operators without changing the paint. My airline used Omni International aircraft to help support network growth and IROP recovery when first introducing the B767. 20 years ago, Canada3000 did the same with some of their Airbus fleet for Air New Zealand (IIRC). Two examples from a litany of examples worldwide.

With that said, an aircraft does have to have the weight of paint included in the weight and balance report (a component of the Basic Empty Weight) and this must be signed off by an aircraft maintenance engineer. This check by the AME must include free and full movement of all flight controls, to ensure the paint does not restrict movement. In the computer-driven age where BEW (more likely OEW) is simply a line item on the flight plan, it's not an issue to have multiple aircraft in multiple liveries. But back in the day of paper flight W&B records, it could be a headache to track which airplane had a higher BEW because of a specific paint scheme.

Finally, the livery is a pretty cheap way to market the airline. It's going to be seen, so may as well show people who it is. The average passenger won't care to look for more than 30 seconds at a special paint if it's not immediately clear who owns it, hence most aircraft in the fleet are painted the same to increase the advertising footprint.