I was wondering if there is a way can completely delete messages from my iPhone? Simple deletion can't erase message at all, it can be easily recovered by some data recovery tools.
If you are going to sell the phone, then i recommend factory resetting the device. You can follow the guidelines provided by Apple:
If you only want to delete the messages, then below is a good article on how to do that.
Alternatively, you can manually delete the messages one by one. However it takes time if the list was long.