Each Patronus is unique

[swapnil_d2727]

No: HPFGUIDX 163873

Yeah it's a nice doubt, but I think as JK says it changes its shape due
to attack or some sorrow resting in your mind which Tonks certainly had
(she loves Lupin)or about Harry who misses his parents so his patronus
has the shape of stag.

But as you say, it can confuse the person if it changes its shape, then
the person not trusting the patronus would immediately send msg to other colleagues & tell them that someone has sent me this shape of patronus, is it yours or not?  So the person whose patronus has changed its shape will immediately come to know this.  And yes, there will be at least one person whose patronus doesn't change. DD must have taken your points into consideration before using patronus to communicate since he is 'cleverest wizard'.

Good bye.
 Love,
 Swapnil_d2727