Solution 1:

The UI does not directly support renaming a Function, but you can work around this using the following manual steps:

  • Stop your Function App. To do this, go under Function app settings / Go To App Service Settings, and click on the Stop button.
  • Go to Kudu Console: Function app settings / Go to Kudu (article about that)
  • In Kudu Console, go to D:\home\site\wwwroot and rename the Function folder to the new name
  • Now go to D:\home\data\Functions\secrets and rename [oldname].json to [newname].json
  • Then go to D:\home\data\Functions\sampledata and rename [oldname].dat to [newname].dat
  • Start your function app, in the same place where you stopped it above In the Functions UI, click the refresh button in the top left corner, and your renamed function should appear
    Note: doing this can lose some historical logging.

Github Issue for renaming Azure Function


Edit for new info

To anyone like myself that arrived here looking to rename their function, despite this being the previously correct answer, there is now a much smoother CMD based process as detailed in this answer by SLdragon and an even smoother GUI based process detailed in this answer by Amerdeep below.

Solution 2:

Now (2017.10) we can use console to rename the Azure Function name

  1. Open the Console from your Function APP -> Platform features:

Open the console

  1. Rename the Function folder using command line:

Rename the folder

  1. Restart the Function:

Restart the function

  1. Refresh

Refresh

Solution 3:

Create a new function and you will have an option to name it, then delete the default one(HttpTriggerCSharp1).

I know it's not renaming, but the easiest option around.

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