Mongodb common key

I have a collection

 [{
 name: xyz
firstname : abc 
lastname: ghs
country : india 
},
 {
  name : fggh
  firstname :bqjdjbw
  lastname :jhhfjk
 }]

Like this array of docs in mongo db, now i need to find a common key in order to optimise my queries right now if i need to find first name and last name i query like this

   db.getCollection("db").find({
  $or: [{name : "xyz" , country:"india"},{name : "cvnb" , 
   country:"india"},]},
   {"first name":1,
   "lastname":1,
   "_id":0 })

Can someone help me how can i find a common key or can i find id or use some algorithm to optimise it since i will eventually have to add in my java code.