If you want to get fancy: systemd credentials. It can store the secrets encrypted on disk and seal the encryption key with the TPM chip. The encrypted secret is decrypted (non-interactively) and made available only to a specific systemd service. The process itself does not special systemd integration–it just sees a plain text file containing the secret, backed by a tmpfs that’s not visible to other processes.
Depending on which TPM PCRs you bind to, you can choose how secure you want it to be. A reasonable/usable configuration would be something like binding to PCRs 7 and 14. With that setup, the TPM will not unseal the key if the system is booted into any other OS (i.e. anything signed with a different UEFI Secure Boot key). But if you really want to lock things down, you can bind to additional PCRs and make it so changing any hardware, boot order, BIOS setting, etc. will prevent the TPM from unsealing the key.
I don’t have any knowledge about the specific containers, but the way this works on my Linux distro is via the:
send host-name "(hostname)";option in
dhclient.conf. Maybe you could try explicitly setting that option?