I am trying to store image from firebase database and named it FirebaseuniqUserID.jpeg.(like buwkgefuikbuifbkc8gfybfy.jpeg). And user can change image anytime. For getting image
You can use two different options, first is Glide and 2nd is that, you can save image downloading status in your local database file or SharePreferences. But image cache is the best solution.
I want avoid downloading if current user has latest updated image of user in Firebase
To solve this, I definitely recommend you to use an image loading and caching library. For Android we have Glide:
Glide is a fast and efficient open source media management and image loading framework for Android that wraps media decoding, memory and disk caching, and resource pooling into a simple and easy to use interface.