In my CDP account, what does settlement date means? Does it means the day the stock I traded is officially under my name?

The date the transaction is settled. It is when you officially paid in cash and receive shares or the official date your shares are sold.

It is the day when you paid for your shares

The settlement date is the date when the trade is final. Here is the full information from Investopedia: https://www.investopedia.com/terms/s/settlement...

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Date that the transfer of share is completed.

I remember it to be 3 days after trading.

But brokers may extend some credit to you if you have some history with them.

Stock will be under your name after that. ​​​