But she was told her marriage would have to be registered using her birth name - Luis Alexander - instead of Eliana.
"It is a black spot to an otherwise very happy occasion for us," said Ms Rubashkyn.
"Whatever it is, I am so excited that I am now a married woman, and that our love is now official."
Ms Rubashkyn said she wanted to use Eliana because she wanted her "male identity" to be a thing of the past.
"I guess it's one of those things for people like me ... our past will always come back to haunt us," she said.
Ms Rubashkyn, originally from Colombia, came to New Zealand as a refugee in May last year.
She was issued with a New Zealand certificate of identity stating her gender as "female" although she had not had sex change surgery.
She chose to move to New Zealand only after she received assurance her gender of preference could be recorded in her travel documents without the need for surgery.
Ms Rubashkyn met Itamar online eight months ago and her mother paid for his ticket to Auckland for the marriage.
Itamar said his family did not approve of their relationship, had threatened to publicly shame him in Israel for "being gay" and wanted to commit him to a psychiatric hospital.
Itamar will lodge a residence visa application under the partnership category, but is still waiting for a police certificate of good character to arrive from Israel.
The couple's wedding at the Registrar of Marriages in Albert St was attended by just two friends, who also acted as witnesses.
They are planning their main celebrations on Tu B'Av, a Jewish holiday similar to Valentine's Day, which this year falls on July 30.
A Department of Internal Affairs spokesman said Ms Rubashkyn was asked for her birth name as a matter of record.
"To maintain public trust and confidence in the marriage register we need to link the names of married parties back to their birth name," he said. "This is to ensure we can be certain of their birth identity no matter how many times the person's current name changes."
The spokesman said Ms Rubashkyn's current name and status as bride would be recorded in the department's records.
More same-sex couples in New Zealand are opting for marriage rather than entering into civil unions, according to Statistics New Zealand.
Asked if Ms Rubashkyn's marriage would be considered a same-sex one, Statistics NZ spokesman Colin Marshall said it depended on what they wrote on their form.
"People self-identify," Mr Marshall said.
"It would depend entirely on what the person wrote on the application forms to marry."
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