I don't know what I'm missing but I'm not able to understand from where the Bone.001 came? there is no other armature and if we create other armature it's bone is also labelled as 'Bone'.
Bone.001 is not inside Bone, it is in the Armature.
To try and explain better, the Armature object is like a skeleton, which contains many bones.
When you first add your Skeleton (Armature), it will start with one bone. To add more bones you enter edit mode and add them with the methods Spikey mentioned.
Yes, it worked and I understand now. Thanks Martin and Adrian.