Usually, favicons are in “.ico” format and named favicon.ico. I have made my own by opening my image in Photoshop, resized it to 16px by 16px and then “Save for Web” as a PNG-8 and saved it. Then I renamed it to favicon.ico instead of favicon.png.
You might also want to check where your site is trying to look for the favicon.ico file. Mine is located under “wp-content > themes > [mytheme]”.