It was really simple, just call:
String model = Build.MODEL;
Update: This code will print the exact string you requested:
String reqString = Build.MANUFACTURER
+ " " + Build.MODEL + " " + Build.VERSION.RELEASE
+ " " + Build.VERSION_CODES.class.getFields()[android.os.Build.VERSION.SDK_INT].getName();
Prints:
Samsung Note 4 6.0 MARSHMALLOW
LGE LG-D410 4.4.2 KITKAT