It's one of my favourite flower names. It's from Old French pensee, 'thought', but already in French applied to the flower, with the sense of a remembrance. Pensee comes from Latin pensare, 'weigh up' and this is where it gets really interesting, because pensare comes from a word pendere connected with weighing or hanging something up.
This in turn goes back to a Proto Indo-European root *(s)pen- which is the ultimate origin of a long list of words, some quite unexpected, such as as dispensary, expensive, peso, penthouse, spider and spontaneous.
I'll finish with a rather touching little poem ca. 1450 I found in the Middle English Compendium.
The lynyng of hit was with nedille wrought..With litille, litille flowris soft, The soven and the daisy, But most of pancy.
Soven must be connected with souvenance (think souvenir) so presumably another flower symbolising remembrance, but I couldn't find what it is. Perhaps we can never know.