I work as an employee in a A 501(c)(3) tax-exempt organization but Paypal 1099-K mentions my name as Payee

Yes, you should contact PayPal to get the name updated on the account and on the form.  If it was not your PayPal account, the Organizations name should be listed instead of yours.

It could create confusion at some point that you would need to straighten out if you leave it as it with your name on it. 

Thank you Vanessa for your response. Really appreciate it.