Can try installing Avahi on the RPi (may come on the default image). It will advertise .local over mDNS / DNS-SD. I believe Avahi will advertise on link local if there is no default route to the internet.
Your system may automatically resolve the domain if its able to pickup the mDNS records to SSH in. Been a couple years since I've done it, so I could be forgetting a nuanced detail, but I vaguely remember just 'plug and play' if internet for the RPi wasn't required.