As I understand the question, OP does not want to clone person2 into a new instance of Person, but is asking for how to copy the contents of person2 into an already existing instance (person1) of Person. There is an overload of AutoMapper’s Mapper.Map method that does this for you:
Mapper.CreateMap<Person, Person>();
Mapper.Map<Person, Person>(person2, person1);
//This copies member content from person2 into the _existing_ person1 instance.
Note 1: @alexl’s answer creates a new instance of Person. If you have other references to the instance that person1 points to, these will not get the (presumably) desired data update if you redirect the person1 variable to a new instance.
Note 2: You need to be aware of that the (recursive) copying depth depends on what mappings AutoMapper knows about at the moment of mapping!
If a member of the Person class is of say the class Brain and you additionally have done Mapper.CreateMap<Brain, Brain>(); before the copy data Mapper.Map<Person, Person>(person2, person1); call, then person1 will keep its current Brain instance but this Brain will receive the member values of person2‘s Brain instance. That is you have a deep copy.
But if AutoMapper does not have a Brain-Brain mapping before copying, then person1‘s Brain member will reference the same Brain instance as the one person2 references. That is you will get a shallow copy.
This applies recursively to all members, so you better make sure AutoMapper has mappings for member classes that you want to deep copy, and doesn’t have mappings for member classes that you want to shallow copy.
An alternative to using AutoMapper would be to use an approach using reflection. (Note that the code in the link does a shallow copy!)
“Support for filling an existing object, instead of AutoMapper creating the destination object itself” was added in AutoMapper version 0.2.