Loaded up my 1.12.2 testing world in 1.13, and found that all the structure blocks it contained no longer had anything listed in the 'structure name' field of their GUI.
All other structure data appeared to remain intact.
Comments 2
After reloading from backup and checking, it appears that the names being removed did all contain upper-case characters (I have a tendency to use CamelCaps when naming things) and changing these names to use all lowercase does allow them to persist through updating.
Turns out I missed the few structure blocks that didn't have their names erased in the shuffle because they weren't displaying the on-mouseover tooltip any more.
What names have you used? Structure names no longer can contain upper-case characters or multiple colons, so that will be cleared.