What should I do if I change my BitCoin wallet? At present, I use Electrum as my wallet, and I create private key and transfer some bitcoin to the Electrum wallet.

If I choose a new  wallet such as  BitGo wallet listed on https://bitcoin.org/en/choose-your-wallet, how can I pass bitcoin from old wallet to new wallet?

Do I must to send bitcoin from old Electrum wallet to the new address created by new BitGo wallet?
When switching wallet providers/programs, the safest option is to usually just send the BTC to the addresses provided by the new system (after you have made a backup of the mnemonic phrase/keys for the new wallet).

Although standards compliant wallets should be able to accept each other's seed phrases, a wallet restoration process is an inherent weak point of the system, leaving you susceptible to attacks such as keyloggers and phishing. Thus, it is better to set up a new wallet.

Note that you should be aware of basic security practices regardless of which method you use, such as ensuring you are on the correct website, using a trusted/ clean device, and making sure that no one is looking over your shoulder.