Is it mandatory for dependent child (H4) to stay with principal applicant (H1B)

[sicorp]

I'm currently in US in H1B. My wife also has H1B & she will be in US sometime soon from India with our child (already has a H4 where my wife is principal applicant). My wife's job location is in different state & we are planning that our child will be staying with me.

Do I need to apply for principal applicant change for my child's H4? OR he can stay with me without changing the H4 principal applicant?

Any information/reference point is appreciated.