In network security, encryption and integrity done by the same algorithm that is AES-CCM in that MIC generated by CBC-MAC and encryption done by CTR mode. So suppose I want to do encryption with any stream cipher algorithm, can I use some hashing mechanism like HMAC separately for integrity purposes?
Yes, and that's how it's normally done. This even applies to AEAD schemes like GCM, CCM, and EAX (which all encrypt with CTR and MAC as a separate matter with some other algorithm); with non-AEAD schemes, you have systems like CBC+HMAC in TLS, and (with stream ciphers for encryption) ChaCha20+Poly1305 (which are two completely independent algorithms). However, this is something that's really hard to get right, which is why standardized AEAD schemes are so nice (AEAD means there's a well-analyzed specification of exactly how to combine them).