Choose a list of dictionaries at random from notes
(using the fact that a dictionary yields its keys when treated as an iterable), then choose a value from the list using the known key "name".
import random
notes = {"raitisu": [{"name": "test"}, {"name": "test1"}],
"iceyyheart": [{"name": "test"}]}
notes_key = random.choice(notes)
random_dict_list = notes[notes_key]
random_value = random.choice(random_dict_list)["name"]
note = { 'name': random_value }