One of two properties is required from the data model

Let's say I have a Person class with FirstName and LastName. I want that the user must enter at least one of the two values in the UI but he may not have to enter each of them.

If I place the Required attribute / data annotation on each of them, that makes both of them required.

How do I make a server side validation (with client side validation, too) for this rule?

You could use a custom attribute for this. In short, the custom attribute will retrieve both values and then ensure at least one has a value. See this page for more information. Here is an example (untested code):

[AttributeUsage(AttributeTargets.Property, AllowMultiple =false, Inherited = false)]
  public class ValidatePersonName: ValidationAttribute
  {
    protected override ValidationResult IsValid(object value, ValidationContext validationContext)
    {
      string FirstName = (string)validationContext.ObjectType.GetProperty("FirstName").GetValue(validationContext.ObjectInstance, null);

      string LastName = (string)validationContext.ObjectType.GetProperty("LastName").GetValue(validationContext.ObjectInstance, null);

  //check at least one has a value
  if (string.IsNullOrEmpty(FirstName) && string.IsNullOrEmpty(LastName))
        return new ValidationResult("At least one is required!!");

      return ValidationResult.Success;
    }
  }

Usage:

class Person{

 [ValidatePersonName]
 FirstName{get;set;}

 LastName{get;set;}
}