Objects are identified during collection updates and merges using members with the following names:

• Id
• <Type name>Id
• Identifier
• <Type name>Identifier

You can configure an object to be uniquely identified with a different member using:

Mapper.WhenMapping
    .InstancesOf<NamedCustomer>() // Apply to NamedCustomer mappings
    .IdentifyUsing(c => c.Name);  // Identify using NamedCustomer.Name

Or, configured inline:

Mapper.Map(customerDtos).ToANew<NamedCustomer[]>(cfg => cfg
    .WhenMapping
    .InstancesOf<NamedCustomer>()
    .IdentifyUsing(c => c.Name)); // Identify using NamedCustomer.Name