To increment the field names you would probably have to use either the calc
macro () if you want fields with only numeric names, or the
action-increment widgtet
(http://inmysocks.tiddlyspot.com/#MathyThing%20-%20action-increment%20Widget)
if you want fields with a prefixed number. If you want more complex field
names you can use string concatenation to build them
(http://inmysocks.tiddlyspot.com/#Concatenating%20text%20to%20make%20dynamic%20URLs).
You would probably do something like make a field called 'count' and
initialize it with 'field-0', then make your button that creates a field
with the name stored in the count field, and then increments the count
field.
something like:
<$button>New Field
<$action-setfield $field={{!!count}} $value=<<whatevervalueyouwant>>/>
<$action-increment $field='count' $increment=1 $prefix='field-'/>
</$button>
the first time you use that it will create a field called 'field-0' and
then change the value of the count field to field-1, the second time it
will create a field called 'field-1' and increment the value to field-2,
and so on.
You can get the same thing from the calc macro if you don't want the prefix
part or use the string concatenation mentioned above.
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