How to convert the following json string to java object?

No need to go with GSON for this; Jackson can do either plain Maps/Lists:

ObjectMapper mapper = new ObjectMapper();
Map<String,Object> map = mapper.readValue(json, Map.class);

or more convenient JSON Tree:

JsonNode rootNode = mapper.readTree(json);

By the way, there is no reason why you could not actually create Java classes and do it (IMO) more conveniently:

public class Library {
  @JsonProperty("libraryname")
  public String name;

  @JsonProperty("mymusic")
  public List<Song> songs;
}
public class Song {
  @JsonProperty("Artist Name") public String artistName;
  @JsonProperty("Song Name") public String songName;
}

Library lib = mapper.readValue(jsonString, Library.class);