Laura Matthews, 29, added the extra name "for a bit of fun".
She has now been asked to return a disclaimer form in order to use "L. Skywalker" as her passport signature.
The Home Office said no decision had yet been made, but it would consider Ms Matthew's application.
Ms Matthews, who lives in Southend, ended up missing a holiday as her passport renewal had not been completed in time for her flight last month.
"It's been an awful mess with many calls in tears to the customer service main line team over the last nine weeks," she said.
A spokesman for Her Majesty's Passport Office said: "The reputation of the British passport is a key factor in ensuring that UK citizens are able to travel freely across borders with minimal hindrance.
"We will not issue a passport in a name which breaches copyright law or which undermines the integrity of the British passport."
A woman whose middle name is "Skywalker" has been told by passport officials her signature might be valid - despite being told last week it was an infringement of copyright.