I have different behaviour with query by example when I enter A in a varchar2 column.

On some machines it generates :deptname like 'A%'
On another: deptname like 'A'
even sometimes:deptname = 'A'

What is the option to control that ?

This behavior is affected by the "Query By Example" preferences (Tools > Preferences > SQL Window tab page). The "Automatic contains" option controls whether A is converted to %A%.