worst case, why not seach by name but return the item #? (not sure what "item #" is)
In the attached screenshots my Dimensin is V629 - Named "Hole2Hole" see the diff Properties for each
I ended up doing this and got it to work...
foreach (SolidEdgeFrameworkSupport.Dimension dimension in cSE.oDimensions)
var name = dimension.DisplayName;
dimension.SubfixString = sTaperInfo;