Assign field names

Hey there!

Is it possible to assign the content of a cell (line layer) in the attribute table to another layer (point layer)? It would be great if this would work automatically so I don't have to do it hundred of times manually.

I've provided a screenshot for better understanding of my problem.
The lines have unique names and i want the (yellow) points on the lines to have the same names.

Is there a way to do this in ArcGIS?

Attached Thumbnails