Yes, your profile is entirely up to you.
You choose your display name, photo, and bio. You choose which social handles to show, at least one, but you decide which. And you can change your visibility settings any time.
Nothing about your profile is locked in. If you want to update your photo, swap a handle, or step back from being visible for a while, it's always in your hands.
Related:
When am I visible to others?
Why do I need to add a social handle?
What can others see about me?