Philip being the name of the DOE, whether he was born a Greek Prince or not, firmly embeds Philip now as a BRF name. There is also Mary I's husband. As with many of the other names, names often come from other countries via marriage. Victoria was introduced by Queen Vic's German mother of the same name. She was named Alexandrina, as Victoria was thought too German for a possible heir to the throne.
Sophie/a has been well established in the BRF, since the Hannoverians came to the throne.
Sophia of Hannover-mother of George I, granddaughter of James VI and I
Sophia Dorothea-daughter of George I, Queen of Prussia
Amelia Sophia- daughter of George II
Princess Sophia of Gloucester-niece of George III, by his brother William
Princess Augusta Sophia-daughter of George III
Princess Sophia-another daughter of George III
Princess Sophie of Prussia, later Queen of the Hellenes-Victoria's granddaughter
Since it has not been prominent but the Earl of St. Andrew's youngest daughter is Lady Amelia Sophia Windsor. Though by marriage, we also have Sophie Wessex, and Lady Frederick Windsor (Sophie Winkleman).
If either Sophie or Philip were chosen, I doubt anyone would not say they chose a royal name, one from the royal family. Yes Mike may have Philip in his family tree, but it's like saying if Will and Kate have a daughter and name her Elizabeth, they are naming her for Kate's middle name/mom's middle name/and Kate's great grandmother.
Other than spellings, or new 'american' inventions, most popular names have old roots to them.