How to set downloading file name in ASP.NET Web API

You need to set the Content-Disposition header on the HttpResponseMessage:

HttpResponseMessage response = new HttpResponseMessage();
response.StatusCode = HttpStatusCode.OK;
response.Content = new StreamContent(result);
response.Content.Headers.ContentDisposition = new ContentDispositionHeaderValue("attachment")
{
    FileName = "foo.txt"
};

EDIT: As mentioned in a comment, My answer doesn't account for characters that need to be escaped like a ;. You should use the accepted answer Darin made if your file name could contain a semi-colon.

Add a Response.AddHeader to set the file name

Response.AddHeader("Content-Disposition", "attachment; filename=*FILE_NAME*");

Just change FILE_NAME to the name of the file.