The name is Handel, not handle. Georg Friederic Handel (1685-1759) was a famous German composerwho spent much time in England. Herbert first met Pip at Miss Havisham's. Pip used to sing songs there and pretend to be beating out the tempo with a blacksmith's hammer, as he did when assisting at the forge at home. I believe Herbert also called Pip "the musical blacksmith." I can't see any special significance, just a friend giving a friend a special nickname. Maybe Herbert thought the name Pip was inappropriate for someone who was to inherit a fortune and become a gentleman.
There was a famous German composer in the late 1600's to mid 1700's named George Friederic Handel. The last movement of Handel's Suite No. 5 in E Major for harpsichord had a name -- "The Harmonious Blacksmith." Herbert nicknames Pip "Handel" because Pip used to sing while working at Joe's forge, using the beats of his hammer to set a tempo for his songs.
Perhaps Herbert nicknamed Pip this because the name "Pip" doesn't sound too gentlemanly? After all, "Handel" does sound much more formal than a simple "Pip."