Change machine name

Hi,

Two machines on the same network

Machine A ( IP : XXX.XXX.XXX.XXX)

Machine B ( IP : YYY.YYY.YYY.YYY)

1. I install the sql server instance ( default instance - machine name B ) in machine B

2. Migrate the database from A to B

3. now shutdown A

4. Change the Machine name and IP address of B with Machine name IP address of A ) so B become A.

My question is after i change the machine name from B to A, Do i still need to update the sql server instance name from B to A to access the sql server with instance name from other machines?