It is just a question of appearance and what you are happy with. When building you don't trim it because you don't want mortar bridging the DPC. Afterwards if you have a bit more showing than you would like then feel free to trim it.
Whilst the other posters are entitled to there opinions It is good practice to have a DPC below copings unless the coping is a lead covered or a metal section as used as sometimes used at high level.
You should use a bitumen based DPC not the plastic ones ^woody^ is correct that the DPC introduces a weak bond. Generally a bitumen based DPC roll will provide a better bond than a plastic.
It would not be necessary if the masonry below was of an engineering quality.
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