Steady rest for turning long shafts

Correct name is "Follow Rest", or lesser used "Travel Rest", as it moves with the carriage.
A variation, being part of the tool holder is a "Box Tool". Very common on small turret lathes, not having means to support with a center.

That said, this is a clever implementation, compared to finding the correct casting for your lathe model and swing.

Steady rest for turning long shafts - video