const regex = /\*\*\[(.+)\]> \[([^*]+)\]/gm; 
  
 const str = `**[Никнейм]> [сообщение]** 
 **[Никнейм2]> [сообщение2]**`; 
 let m; 
  
 while ((m = regex.exec(str)) !== null) { 
     if (m.index === regex.lastIndex) { 
         regex.lastIndex++; 
     } 
      
     if(m.length < 3) continue; 
     const nickname = m[1]; 
     const message = m[2]; 
     console.log(nickname); 
     console.log(message); 
 }