A common solution is to configure your systems with an (extra) search domain.
The domain search list is used by a resolver to create a fully qualified domain name (FQDN) from a relative name, i.e. when you type somehost
and that can't be foun (there is for example no such entry in your hosts file) the resolver will attempt to find if a somehost.default.svc.cluster.local.
FQDN exists by appending the default.svc.cluster.local search domain. If it does it will behave as if you had entered somehost.default.svc.cluster.local.
The relative name can't contain a .
dot and a domain search list with multiple domains may not always work as you'd hope either.
Regarding your use of .local
DNS name:
if you want to obfuscate your domain use the reserved example.com.
or similar domains.
Please do not use the .local
TLD your for internal DNS records, but only for its intended purpose.
For internal DNS records, please use a subdomain under your own domain, (or a dedicated domain you actually own) instead.
Do not add '.local' to your search domain