If you're coming to this help article with the question "Can you change your name in Stardew Valley?" in mind, I think the answer would be dependent on what you're actually asking.
To clarify, if you are wondering whether Stardew Valley has a built-in feature to change your name - the answer is no, it doesn't (at least right now, in 2018). If you're looking to change your name in Stardew Valley, but don't mind doing so by changing your save files manually, then the answer is yes - it is possible!
The only catch is that this only works for Windows and Mac - if you want to change your name on Nintendo Switch, XBOX One or PS4, at the moment that isn't possible. But, if you're looking to change your name for the purpose of spawning in items, there are other methods you can use to cheat items into the game - see our spawning items guide instead!
First, make sure your Stardew Valley game is closed. You're then going to want to navigate to where your save files are stored:
On Windows, they're located in %AppData%, you can do this by opening up an Explorer window an typing %AppData% in the address bar (illustrated below).
On Mac, you will need to visit "/Users/[Your Mac Username]/.config/". You may have to enable hidden files to access this folder, to do this, press COMMAND + SHIFT + . inside your Finder window.
You'll then want to navigate to the "StardewValley" folder and then go to the "Saves" folder, this is the same on both Mac and Windows.
After entering the Saves folder, go into the folder that is named after the character you want to modify the name of, followed by a bunch of numbers. In the below example, we are changing the name of a character who is currently called "JohnDoe":
Open up the file that is named "SaveGameInfo" (with Notepad or your preferred text editor) and use CTRL + F or COMMAND + F to search for the name of your character. You should find the name of your character in between <name> and </name> like so:
Simply change that name to whatever name you want and save the file and you're done. The next time you open up the game and load your save, your name will be changed.
If the old name is still showing in the saves menu (but not in-game), you will need to change the name of the folder the SaveGameInfo file is stored within.