Presently, there is no feature in Simulink to set a specific height before the inport/outport naming starts.
One workaround you could use if you want your blocks to be as small as possible, without the names clashing is to remove the name of the block from inside the block.
You could refer the block using the automatic names such as the "Subsystem Reference" written in Blue under the block. Automatic names only comes when you hover over the block.