under someone's/something's name
idiom
1
                    
                                          
              
            
                  —used to say that something officially or legally belongs to a specified person
We both own the house, but the car is under my name.
    
                
                    2
                    
                                          
              
            
                  —used to say that something has or uses the name of a specified person
I made the dinner reservations under your name.
    
                
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  Merriam-Webster unabridged




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