AirDrop name on MacBook

Good afternoon, I have recently changed my name legally and of course updated my e-mail address, my Apple ID etc. When I AirDrop documents and pictures from my MacBook to my iPhone, my phone AirDrop name shows as my old name on my MacBook. I have not yet found a way to change this, can someone please help me with this? As mentioned before, my name has been updated on my Apple ID.