See Style Guidelines and this discussion.
In short:
Generally, use the name the artist mainly performs under as the artist name. Alternative names, including any legal names and name variations, should generally be entered as aliases, and can be used in artist credits and relationship credits when appropriate.
So if the artist mainly performed under the name “Phil Gould”, than according to the quoted Style Guidelines you shall rename him to “Phil Gould” and enter “Philip Gould” as an alias.
Sure, you could change the name yourself. Open the artist’s page, choose the “Edit” tab and change whatever is required. Please do not forget to add a note to your change describing why you are applying it. Provide external references, if possible.