Add async task name as option to callsite (#693)

[PrieJos]

Summary

Proposal to add taskName as a callsite parameter (see issue #693).

Pull Request Check List

• [X] Do not open pull requests from your main branch – use a separate branch!
  • There's a ton of footguns waiting if you don't heed this warning. You can still go back to your project, create a branch from your main branch, push it, and open the pull request from the new branch.
  • This is not a pre-requisite for your pull request to be accepted, but you have been warned.
• [X] Added tests for changed code.
  • The CI fails with less than 100% coverage.
• [X] New APIs are added to our typing tests in api.py.
• [X] Updated documentation for changed code.
  • [X] New functions/classes have to be added to docs/api.rst by hand.
  • [X] Changed/added classes/methods/functions have appropriate versionadded, versionchanged, or deprecated directives.
    • The next version is the second number in the current release + 1. The first number represents the current year. So if the current version on PyPI is 23.1.0, the next version is gonna be 23.2.0. If the next version is the first in the new year, it'll be 24.1.0.
• [X] Documentation in .rst and .md files is written using semantic newlines.
• [X] Changes (and possible deprecations) are documented in the changelog.
• [X] Consider granting push permissions to the PR branch, so maintainers can fix minor issues themselves without pestering you.