The reason I’ve always oreffered it when the Perfect Court Tatoos are displayed as Roman numerals is because it’s such a good, yet small way to display Neil’s non-conformity with the rest, and how leaving his father’s home changed him into someone more rebellious.
Initially (by which i mean, when he went to the Edgar Allan Trials when he was 10) he was meant to the 3, or III - which fits the theme of ‘fitting in’ with Kevin and Riko, who also have tattoos only made up of I’s. However, when he runs, Jean instead takes the spot of 3, meaning that Neil would now be IV.
Changing / removing his II tattoo is painted as a HUGE moment for Kevin, as it finally disconnects him from something that has been an unwilling, yet huge part of his image for years, and I believe that Neil’s number being changed has a similar effect for him.
Neil is never shown to be (outwardly) particularly scared of Riko (obviously he is afraid of the Moriyama’s, but not so much Riko alone), which separates him from the other members of the court.
Alongside this, the fact he got away also shows his disconnect from the identity of ‘Perfect Court’.
His refurbished number not fitting the symmetry of the other members of the Court is such a great representation of his bold personality and how he does not fit the identity expected of a member.