You cannot change the name of the load balancer because it will break the sites that use the load balancer.
The ELB has an associated host name that looks like this:
${balancer_name}-${opaque_identifier}.${region}.elb.amazonaws.com
( ${opaque_identifier} is assigned by the ELB initialization infrastructure to disambiguate ELBs with the same name, belonging to different accounts, but have no documentary external meaning.)
Renaming the load balancer, if enabled, would necessarily change this host name, namely, how the sites point to the balancer using CNAME or A -record aliases (in route 53) ... and which would destroy the sites, since then they would point to a non-existent host name.
The simplest solution is to create a new balancer with the name you want using the same configuration, and then transfer to it: for old work, which still functions normally, attach the new balancer to the same back end, wait until they show " in the service "... test ... then change the DNS records pointing to the old balancer to point to the new balancer ... wait for the TTL on the old DNS records elapse, for the new balancer to pick up traffic, and for the old balancer don't show traffic in Cloudwatch metrics ... check the behavior ny ... then remove the old balancer.
Having the same set of instances connected to multiple ELBs is a supported configuration, so you should not have any transient problems with this if you set up a new balance, identical to the old one, with the same subnets, security groups, listener configurations, and etc.
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