Different surname - Naturalisation AN Form Advice

[AussieInLondon]

Hi there

I have an Australian passport (by birth) as well as a Greek Cypriot passport (by heritage) and have been living in the UK for 15 years. I'm currently looking to complete my naturalisation forms to become a British Citizen (because of Brexit) and need some advice.

The English surname shown in my Cypriot passport is different to my birth surname used in my Australian passport and all my other documentation (they spelt my name phonetically rather than a proper translation...)

I would like my naturalisation to reference my Australian surname, however, my EEA permanent residency card shows my Cypriot surname. Is this an issue? Can I complete the entire form using my Australian surname and still reference my EEA permanent residency card in section 2.4, despite the difference?

Thanks!