Include task "task _run_name" dynamically & batch wise running the task based on m/c resource

I have created a task and inside a flow & using the map function.(based on this Tasks - Prefect Docs)

  1. I would like to change my Task name dynamically based on the input i give to my Task.
    Here I gave dict as an input to the task & i want to use a key from the dict to update its
    how can i achieve this ?

  2. Also, I have 1000’s of dicts and I if i run this, all the 1000 dict run as separate task, which is difficult to manage & the visualization in UI will not be appealing. So Can we do it batch based on the resource available in my machine, so that i can see the first few batches running in UI and after one job finished take the next task and so on …?

Please note that, I don’t want to change my below code format, since it breaks many things.

Code example

class Pipeline:
    def __init__(self):

    def run(self, doc):
        # do something with doc 
        # & update the task name from doc
        task_run_name = doc['id']

class PrefectRunner:
    def __init__(self, pipeline: Pipeline):
        self.pipeline = pipeline

    def run(self):
        # contains list of dict
        dict_docs = [
            {"doc": "doc1", "id": 1},
            {"doc": "doc2", "id": 2},
            {"doc": "doc3", "id": 3},
        task_run = task(self.create_task_run_from_flow)

    def create_task_run_from_flow(self, doc):