There is only one legal way to change ones name in England and Wales and that is to use the new name.
Deed Poll - correct name Deed of Change of Name - is simply a system to record changes that have been made, it does not in itself change the name.
Other forms of evidence of change of name include
a statutory declaration
a public announcement (e.g. an announcement in a newspaper)
a letter from a responsible person (e.g. a GP, solicitor, minister, priest or MP)
The most common change of name comes about by marriage.
Cheers
Guy