No, you do not need to sign a cover letter submitted electronically. Hiring managers won’t notice or care if a cover letter is or isn’t signed.
It is enough to just type out your full name after you sign off with an appropriate close like “Sincerely,” or “Kind regards,”.
You can add a custom electronic signature to your cover letter, or scan your application with a handwritten signature, but it’s unnecessary and 100% not worth your time.
(Unless you are famous – then they might want to hang your signature on a wall. Then you should probably include a photo as well).
