how can a function find the name by which it is called?

[Gribouillis]

with this i would need to parse the line (not too hard) and determine which name this call was (much harder).

You can walk a line with the ast module to find all the expressions that were called in the line

>>> line = "print(f'woot {foo()},{bar(456)}',flush=True)\n"
>>> import ast
>>> p = ast.parse(line)
>>> for node in ast.walk(p):
...     if isinstance(node, ast.Call):
...         print(ast.unparse(node.func))
... 
print
foo
bar

other example

>>> line = "xyz[0](spam, bar.x[1].egg(3))"
>>> p = ast.parse(line)
>>> for node in ast.walk(p):
...     if isinstance(node, ast.Call):
...         print(ast.unparse(node.func))
... 
xyz[0]
bar.x[1].egg

Note: ast.unparse() needs Python >= 3.9. For earlier pythons, there is an «astunparse» module in Pypi.