What do I need to do to replace this shower faucet handle?
When it comes to trim kits for mixer valves, the method of attaching them can differ a lot between manufactures.  If you can get the model number of the mixer valve and/or trim kit (trim kit is the handle and escutcheon plate, usually sold together) you can go to the manufactures catalog and see if;

1) different handles are available for the trim kit  or

2) select a different trim kit with the handle you like. Most mixer valves will work with various trim kits from the same manufacturer.

At most box stores, they only display complete kits, mixer and trim together, however a knowledgeable sales person will know how to use the manufacture's catalog to select different trim kits to work with your mixer.