I just tried in my emulator, v6.5.1.1, and I am not seeing anything for line names. We only have one person, our senior surveyor, using Survey Pro so I cannot speak too much on it.
He uses it primarily for points like you mention your crews do. I do know it will handle the same files and surfaces that I supply to SCS900/Siteworks.
I know for SIteworks, I name my lines what ever the layer is. Are you aggregating this data more or could you use layers instead? It looks like it does a good job of show layers especially in areas where you may select on more than one line.

The emulator is available here and you can run it in demo mode: Trimble Docushare