Your address for Bitcoin and Bitcoin-based crypto assets changes every time you receive a transaction. For other crypto assets (Ethereum, XRP, Stellar, etc.) the address stays the same.
Bitcoin transactions are public information. Addresses should not be re-used for better privacy. Ledger Live automatically generates new addresses using standards (BIP32/BIP39/BIP44) and keeps track of your previous ones. Previous addresses do remain valid, but they don't offer an optimal level of privacy.
How it works
Each of your crypto assets accounts has an extended public key, called an xpub. From this extended public key all your public addresses for that account are generated. Thanks to the xpub you can receive transactions on a new address that belong to the same account.
You can find the xpub of an account in Ledger Live by clicking the wrench icon on the account page. In the Edit account window, check the advanced logs.