Pontederia cordata = Bluepickerel = Blue Pickerel = Pickerelweed
The first name is the scientific name and the others are common names. A plant can have many common names but it will always only have one scientific name.
I grow this plant. I have about 20, possibly more. I have also recorded them in the wild as they really are a North American native. They are pretty much always found in what would best be described as muck with only about an inch or two of fresh water flowing over the top of them. Emergents/Marginals are found in what would best be described as a transitional zone between aquatic and terrestrial. Sink these plants too deep and try to grow them as an aquatic and there could be issues in the long run.
In the spring before other species begin active growth, they sometimes receive full sun however as summer progresses and companion species and other same species plants begin to take off and fill in with lush sun-blocking vegetation, the plants usually only receive filtered sun. Perhaps this is why the tag says both full sun to filtered sun? I've seen these plants burn if they get full afternoon sun in summer.
A happy plant flowers from mid summer until the end of the season. One of the reasons why I like them so much is because they are repeat bloomers. There's also a white form of this plant which looks really great. I wish I had the white form.
When I look closely at your third photo, I'm seeing white flecks. I don't know what those are but best guess is some sort of a pest. When I enlarged your image, I noticed the white flecks seemed to be embedded into the plant leaves. I've never seen white flecks on a Pontederia cordata before. I also noticed that there was what appeared to be black (bacteria and fungi) in the leaves which is normally associated with the plant dying back or rather entering dormancy, it's just a part of the decomposition process. Normally when these plants die back at the end of the season, the leaves turn yellow as if they are getting too much water then the edges sometimes get crispy before they get mushy and start rotting. Sort of like celery that freezes. It's only June though right now and this doesn't normally happen until sometime in October so I'm somewhat puzzled by dieback at this time of year combined with those white flecks.
Temperate pretty much means its from an area that has seasons so it dies back every year just like deciduous trees drop their leaves every fall. This plant normally begins dieback once the temps begin to drop which coincides with shorter days (reduced photoperiod). I don't know how long you have had this plant but you might want to consider wrapping its roots in damp sphagnum and tossing it in your refrigerator this coming fall. Let it "over winter" in cooler temps until next spring or perhaps move it to a location where temps will be around 40F or 3-5C. Sometimes I dust roots with a little bit of sulfur powder when I have to stick them in a frig to provide a dormancy for them.
Best wishes to you with your plants. They really are beautiful and the blooms are great.