Line-neutral vs Line-Line same voltage
Assuming you have a traditional, isolated transformer with separate primary and secondary windings, the output of your transformer as currently configured is floating, meaning that while there is 120V between line1 and line2, the voltage from either of those to ground could be anything, and can change over time.  If you want to make it a traditional hot/neutral setup, you can bond one of the two output lines to ground.  If you're wiring this as the input into a breaker panel, make the bond there -- this makes it a main service panel, from a separately derived service, rather than a subpanel.  The bonded lead then becomes your neutral, and the other is your 120V hot.  

If instead your transformer is really an autotransformer, where the primary and secondary windings are actually the same thing, then you cannot ground one of the outputs.  In this case, the voltage is not floating, but where exactly it is depends on the transformer's construction.  I'd recommend measuring from each of the hot leads to ground to see if one of them is at 0V already, or if they are each approximately 60V from ground, or something else.

To check if it's an autotransformer or a regular transformer, check if there's any continuity between the primary windings (input) and secondary windings (output).  If there is, then it's an autotransformer.