The only things you can change are:
Place pin names inside vs outside (for all pins of the symbol with one setting. Sadly not individually)
name offset (for all pins of the symbol with one setting. Sadly not individually. Ignored if names are on the outside.)
Font size (per pin)
I don’t quite get how the wire can go through the pin name (or number)
Did you perhaps rotate the pin in the wrong direction? (The small circle is where the wire connects. It should always point towards the outside of the symbol.)