How to generate different public keys for each user in a system using openssl in linux?

Question

I want to generate private public key pairs for each user(multiple users) in the system. I have the below code to generate that

    RSA *rsa = RSA_new();
    BIGNUM *bn = BN_new();
    BN_set_word(bn, RSA_F4);
    // We are assuming the PRNG is automatically seeded
    // (should be the case if system has /dev/urandom)
    RSA_generate_key_ex(rsa, NUM_BITS, bn, NULL);
    BN_free(bn);
    FILE *f = fopen("private.txt", "w");
    PEM_write_RSAPrivateKey(f, rsa, NULL, NULL, 0, NULL, NULL);
    f = freopen("public.txt", "w", f);
    PEM_write_RSAPublicKey(f, rsa);
    fclose(f);
    RSA_free(rsa);

But here for each user it generates the same key pairs I don't have any unique identifier for each user. I'm wondering if its possible to generate different keypairs for each user?.