With dns of site to site

Hello
I am set up a network of site to site form home to company。
and dns set as below
https://openwrt.org/docs/guide-user/services/vpn/ipsec/strongswan/site2site
But only make icmp request through FQDN, not computer name

What is the output of uci export dhcp ?
And can you give an example of what should work and what doesn't?

This is the expected behavior.

Is there a way to ping the computer name

Yes.

Host name + domain name.

E.g. - skveen-desktop.lan

(You should be able to set .lan as the search domain - if you insist on using a non-FQDN to reach hosts.)