The default Connection Manager layout does allow some modifications including removing and adding columns. The width of columns can also be manipulated since the column names are based on the field alias name.
Columns I can remove
Any column where the field model name FIBERCONNECTIONDISPLAYFIELD can be assigned. Unassigning this field model name removes the column from Connection Manager. The following fields/columns can be removed using this method.
CableName for FiberOptic Cable
PortType column for F_DevicePort, F_SplitterInputPort, and F_SplitterOutputPort
SlotPosition column for F_PatchPanelCardPortName for F_PassiveSplitPort and F_PassiveCommonPort
ShelfName for F_Shelf
LocationDescription for SplicePoint
Modifying column width
The column names in Connection Manager are the field/column aliases defined for that field. Where the column name includes a underscore like BackPort_Num the column name is a combination of the object alias and a field alias in the object where an object is either a feature class or table. Changing the alias name will change the Connection Manager column name. This will of course change the alias name everywhere in the geodatabase.
BackPort_Num: Backport is the F_BackSidePort table alias. Num is the alias for the F_BackSidePort PortNumber field.
PL_Name: PL is the PatchLocation feature class alias. Name is the alias for the PatchLocation Name field.
PPCard_Position: PPCard is the F_PatchPanelCard table alias. Position is alias for the F_PatchPanelCard Position field.
Strand_Num: Strand is F_Fiber table alias. Num is alias for the F_Fiber FiberNumber field.
FiberCable_Name: Fibercable is FiberOpticCable feature class alias. Name is alias for the FiberOpticCable CableName field.
BufferTube_Color: BufferTube is F_BufferTube table alias. Color is alias for the F_BufferTube field.
Strand_Color: Strand is F_Fiber table alias. Color is alias for the F_Fiber FiberColor field.
What cannot be modified or set in Connection Manager
Cannot change the column order.
Cannot fix the column width where it will persist.