Yes, it is possible to a degree of some certainty to identify the type of hash algorithm that was used.
One tool that I use a lot to do this is hash-identifier.
For example, I create a hash of the Hash_ID.py file:
$ openssl sha -sha256 Hash_ID.py 
SHA256(Hash_ID.py)= 5382a8826c972f8fa8687efe1f68e475c02af4bf542b0d7e68b9deffd388db96
When running Hash_ID.py it will ask for the Hash to be entered:
$ python Hash_ID.py 
   #########################################################################
   #     __  __                     __           ______    _____           #
   #    /\ \/\ \                   /\ \         /\__  _\  /\  _ `\         #
   #    \ \ \_\ \     __      ____ \ \ \___     \/_/\ \/  \ \ \/\ \        #
   #     \ \  _  \  /'__`\   / ,__\ \ \  _ `\      \ \ \   \ \ \ \ \       #
   #      \ \ \ \ \/\ \_\ \_/\__, `\ \ \ \ \ \      \_\ \__ \ \ \_\ \      #
   #       \ \_\ \_\ \___ \_\/\____/  \ \_\ \_\     /\_____\ \ \____/      #
   #        \/_/\/_/\/__/\/_/\/___/    \/_/\/_/     \/_____/  \/___/  v1.1 #
   #                                                             By Zion3R #
   #                                                    www.Blackploit.com #
   #                                                   Root@Blackploit.com #
   #########################################################################
   -------------------------------------------------------------------------
 HASH: 5382a8826c972f8fa8687efe1f68e475c02af4bf542b0d7e68b9deffd388db96
Possible Hashs:
[+]  SHA-256
[+]  Haval-256
Least Possible Hashs:
[+]  GOST R 34.11-94
[+]  RipeMD-256
[+]  SNEFRU-256
[+]  SHA-256(HMAC)
[+]  Haval-256(HMAC)
[+]  RipeMD-256(HMAC)
[+]  SNEFRU-256(HMAC)
[+]  SHA-256(md5($pass))
[+]  SHA-256(sha1($pass))
The way Hash ID works is by checking the hash given against criteria for all the hash types it supports and will give a list of possible hash types.