Yes, all password managers should be able to generate unique new passwords. You can also import existing passwords, but just make sure that they're strong — ideally, that means using some sort of generator, even if it's not the one in your password manager. As you're setting up your new password manager, it's a good time to change any weak passwords.
You can also generate random passphrases with some password managers. While you should use passwords for most of your accounts, passphrases are an alternative if you need something that is more memorizable. A passphrase is usually several words strung together, versus the product of a password generator, which is random letters, numbers and symbols.