How can you add custom supply symbols in Eagle?
You need to change the pin name of the symbol to the desired net name. Symbol, device names are less important here. Here's more info (pasted directly from Eagle 7.2 manual, sect.8.5):


  8.5 Supply Symbols
  
  Supply symbols, such as might be used in the schematic for ground or VCC,
  are defined as Devices without a Package. They are needed for the automatic
  wiring of supply nets (see page 127).
  The following diagram shows a  GND symbol  as it is defined in one of the
  supplied EAGLE libraries.
  Note that when defining your own supply symbols, the pin and the Device
  name need to agree.
  The pin is defined with direction  sup and has the name GND. This specifies
  that   the   Device   containing   this   Symbol   is   responsible   for   the   automatic
  wiring of the GND signal. The text variable for the value (>VALUE) is chosen
  for the labeling. The Device also receives the name GND. Thus the label GND
  appears in the schematic, since by default EAGLE uses the Device name for
  the value.
  It   is   very   important   that   the   labeling   reproduces   the   pin   names,   since
  otherwise the user will not know which signal is automatically connected.
  The pin parameter Visible is therefore set to off, since otherwise the placing,
  orientation and size of the pin name would no longer be freely selectable.
  Directly labeling with the text GND would also have been possible here. With
  the   chosen   solution   however,  the   Symbol   can   be   used   in   various   Devices
  (such as for DGND etc.).



I suggest reading the whole section, it's less than 2 pages long.