If I have a private nameserver in conjunction with a domain I own (i.e. mydomain.net & ns1.mydomain.net + ns2.mydomain.net) and multiple (other) domains at a shared hosting service use these private nameservers, do these private nameservers need to be reconfigured / reinstalled if I switch mydomain.net from one registrar to another?

This sounds like a dumb question (even to me) but I'm having a senior moment right now!

This sounds like a dumb question (even to me) but I'm having a senior moment right now!

I get those senior moments myself from time to time.

Without going into lengthly detail, short sweet answer is no.

DZ is right (as usual)... normally, these private nameservers transfer from registrar to registrar without any problems.