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Here are two routines, one to read the computer name and the other to set it. 

function GetPCName: string;
var
  buffer: array[0..MAX_COMPUTERNAME_LENGTH + 1] of Char;
  Size: Cardinal;
begin
  Size := MAX_COMPUTERNAME_LENGTH + 1;
  Windows.GetComputerName(@buffer, Size);
  Result := StrPas(buffer);
end;

function SetPCName(AName: string): Boolean;
var
  PCName: array[0..MAX_COMPUTERNAME_LENGTH + 1] of Char;
  Size: Cardinal;
begin
  StrPCopy(PCName, AName);
  Result := Windows.SetComputerName(PCName);
end;

SetPCName will fail unless the current user has administrator rights.