DD doesn't have a middle name; neither DH nor I have one so we really didn't see it as important. We more or less forgot! However, if a name had occurred to me which would have gone well with her name, we would have given her one. There is a name which my mum suggested as a middle name for DD which I absolutely would have gone with, but she suggested it too late.
It's completely up to you how and what you name your child but please don't make the mistake my parents made both my dad and my brother have the same first initial and no middle name .... So far they have had 30 yrs of confusion when receiving post and even official problems when they were confusingly issued the same NI number (apparently both having same single initial and address was too complicated for HMRC)
It's up to you, and of course it's not necessary, but I would echo the previous post about caution with authority, who cannot cope with anything so shocking as someone having the same initial! If you have a fairly common surname and go for a conventional first name you will be hounded by credit collectors and grilled at passport control. Our surname is supposed to be the 3rd most common in the UK and my poor OH David has had to 'prove' who he is so many times, often only getting out of it with his 2 middle names which are also not unusual but at least in combination they are! I would make sure the initials are different for the whole family myself, but that's just me!
Nyx ... Might not be such an issue for a girl because you usually have different prefixes ... My dad and brother are both Mr A Wonky. Bothers my brother the most especially when my dad accidentally opens his mail.
No middle names here for our two DC: partly because we've given them two surnames (mysurname hissurname) and we thought a middle name would make it a bit over the top. I don't have a middle name and not does my brother, partly because my dad and my older sister both dislike their middle names.