Long story short: I've screwed up the line running from my accumulator down into the firewall box, creating a hairline fracture in the metal. I've yet to take the box off and find out if it's worth my time trying to take this line out and buy a replacement, so I need a name to look online.

Is there a specific name/model for this line, and has anyone had experience in replacing it in the past?

 

Post a pic.

Sounds like the one that's part of the evaporator, actually; not really a "line" on its own.