Problem:

I created a terrain model using the Create Terrain Model by Graphical Filter tool. This worked fine. However, when I exported the terrain model to a DTM, the DTM did not retain the feature names or feature definitions.

Solution:

If using a Graphical Filter to create the terrain model, you will need to toggle on the option for "Link to Terrain Features" in the Terrain Filter Manager. Doing so will allow the features to retain their names and feature definitions when they are exported to a native format.