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On DNS servers which have record(s) for the old name, change both the forward and reverse data files.
In Blue Light, at least rose runs this sort of DNS service (backupserver's DNS service is caching only)When the hostname of a system on the Blue Light LANs (192.168.10.0 and 192.168.28.0) is changed, the DNS service on backupserver will need re-configuring as documented in DNS server (bind) administration.
/etc/hosts files
On computers with an /etc/hosts file which has record(s) for the old name, change the line.