Assuming you have people is List of object 
  Map<String, String> phoneBook=people.stream()
                                        .collect(toMap(Person::getName, Person::getAddress));
Now you need two steps :
1) 
people =removeDuplicate(people);
2) 
Map<String, String> phoneBook=people.stream()
                                        .collect(toMap(Person::getName, Person::getAddress));
Here is method to remove duplicate 
public static List removeDuplicate(Collection<Person>  list) {
        if(list ==null || list.isEmpty()){
            return null;
        }
        Object removedDuplicateList =
                list.stream()
                     .distinct()
                     .collect(Collectors.toList());
     return (List) removedDuplicateList;
      }
Adding full example here
 package com.example.khan.vaquar;
import java.util.Arrays;
import java.util.Collection;
import java.util.List;
import java.util.Map;
import java.util.stream.Collectors;
public class RemovedDuplicate {
    public static void main(String[] args) {
        Person vaquar = new Person(1, "Vaquar", "Khan");
        Person zidan = new Person(2, "Zidan", "Khan");
        Person zerina = new Person(3, "Zerina", "Khan");
        // Add some random persons
        Collection<Person> duplicateList = Arrays.asList(vaquar, zidan, zerina, vaquar, zidan, vaquar);
        //
        System.out.println("Before removed duplicate list" + duplicateList);
        //
        Collection<Person> nonDuplicateList = removeDuplicate(duplicateList);
        //
        System.out.println("");
        System.out.println("After removed duplicate list" + nonDuplicateList);
        ;
        // 1) solution Working code
        Map<Object, Object> k = nonDuplicateList.stream().distinct()
                .collect(Collectors.toMap(s1 -> s1.getId(), s1 -> s1));
        System.out.println("");
        System.out.println("Result 1 using method_______________________________________________");
        System.out.println("k" + k);
        System.out.println("_____________________________________________________________________");
        // 2) solution using inline distinct()
        Map<Object, Object> k1 = duplicateList.stream().distinct()
                .collect(Collectors.toMap(s1 -> s1.getId(), s1 -> s1));
        System.out.println("");
        System.out.println("Result 2 using inline_______________________________________________");
        System.out.println("k1" + k1);
        System.out.println("_____________________________________________________________________");
        //breacking code
        System.out.println("");
        System.out.println("Throwing exception _______________________________________________");
        Map<Object, Object> k2 = duplicateList.stream()
                .collect(Collectors.toMap(s1 -> s1.getId(), s1 -> s1));
        System.out.println("");
        System.out.println("k2" + k2);
        System.out.println("_____________________________________________________________________");
    }
    public static List removeDuplicate(Collection<Person> list) {
        if (list == null || list.isEmpty()) {
            return null;
        }
        Object removedDuplicateList = list.stream().distinct().collect(Collectors.toList());
        return (List) removedDuplicateList;
    }
}
// Model class
class Person {
    public Person(Integer id, String fname, String lname) {
        super();
        this.id = id;
        this.fname = fname;
        this.lname = lname;
    }
    private Integer id;
    private String fname;
    private String lname;
    // Getters and Setters
    public Integer getId() {
        return id;
    }
    public void setId(Integer id) {
        this.id = id;
    }
    public String getFname() {
        return fname;
    }
    public void setFname(String fname) {
        this.fname = fname;
    }
    public String getLname() {
        return lname;
    }
    public void setLname(String lname) {
        this.lname = lname;
    }
    @Override
    public String toString() {
        return "Person [id=" + id + ", fname=" + fname + ", lname=" + lname + "]";
    }
}
Results :
Before removed duplicate list[Person [id=1, fname=Vaquar, lname=Khan], Person [id=2, fname=Zidan, lname=Khan], Person [id=3, fname=Zerina, lname=Khan], Person [id=1, fname=Vaquar, lname=Khan], Person [id=2, fname=Zidan, lname=Khan], Person [id=1, fname=Vaquar, lname=Khan]]
After removed duplicate list[Person [id=1, fname=Vaquar, lname=Khan], Person [id=2, fname=Zidan, lname=Khan], Person [id=3, fname=Zerina, lname=Khan]]
Result 1 using method_______________________________________________
k{1=Person [id=1, fname=Vaquar, lname=Khan], 2=Person [id=2, fname=Zidan, lname=Khan], 3=Person [id=3, fname=Zerina, lname=Khan]}
_____________________________________________________________________
Result 2 using inline_______________________________________________
k1{1=Person [id=1, fname=Vaquar, lname=Khan], 2=Person [id=2, fname=Zidan, lname=Khan], 3=Person [id=3, fname=Zerina, lname=Khan]}
_____________________________________________________________________
Throwing exception _______________________________________________
Exception in thread "main" java.lang.IllegalStateException: Duplicate key Person [id=1, fname=Vaquar, lname=Khan]
    at java.util.stream.Collectors.lambda$throwingMerger$0(Collectors.java:133)
    at java.util.HashMap.merge(HashMap.java:1253)
    at java.util.stream.Collectors.lambda$toMap$58(Collectors.java:1320)
    at java.util.stream.ReduceOps$3ReducingSink.accept(ReduceOps.java:169)
    at java.util.Spliterators$ArraySpliterator.forEachRemaining(Spliterators.java:948)
    at java.util.stream.AbstractPipeline.copyInto(AbstractPipeline.java:481)
    at java.util.stream.AbstractPipeline.wrapAndCopyInto(AbstractPipeline.java:471)
    at java.util.stream.ReduceOps$ReduceOp.evaluateSequential(ReduceOps.java:708)
    at java.util.stream.AbstractPipeline.evaluate(AbstractPipeline.java:234)
    at java.util.stream.ReferencePipeline.collect(ReferencePipeline.java:499)
    at com.example.khan.vaquar.RemovedDuplicate.main(RemovedDuplicate.java:48)