Does encryption hide file name and hash?
Encryption is performed on the contents of the file, not on the name of the file. After the encryption, you need to save it in a file. Choose whatever name is appropriate. If you want to keep the original filename secret then, prepend it to the plaintext with a proper delimiter so that during decryption, you can get the file name correctly.
Or simply create a Zip archive with a different name, or better use a small Veracrypt volume.
hash; you mean that you also created the hash of the file. Hash is also a file, the same applies as above. Append the hash at the end of the plaintext
plaintext = file name | delimiter | contents of the file | delimiter | hash of file
Your biggest problem with this is how the user will correspond the ciphertext files to original files. Do they need to decrypt and check every file? VeraCrypt solution can be better especially since the files are small.
Does encryption also hide file hash?
If you encrypt a file, then one can no longer find the hash of the unencrypted file.
Can such cloud providers identify the files by their names or hash if they are encrypted?
Assuming the hash is not encrypted, stored together with the encrypted file.
Of course, they can identify some, especially they are also in the public domain. Microsoft build a system (PhotoDNA)) so that they make a hash of every image on a system and compare them on their database and warn the official if a sensitive image is found. It is a service that works. Hash leaks information about the file!
As you can see, the check is based on the availability of the file on the adversary.
The filename may indicate some information about the contents of files. Keep your tracks as minimum as possible!
If you encrypt the file and their hashes with probabilistic encryption and choose a new key for every update they will have no idea about the contents, assuming the file names are encrypted as above. Still, the VeraCrypt volume beats.
Your choices for encryption start from AES-CBC, AES-CTR which has IND-CPA security to AES-GCM, AES-GCM-SIV, xChaCha-Poly1305 i.e. our modern authenticated encryption modes.