If you are in the middle of executing a function and you need to know the name of the function, then you need to use dbstack(). Note that anonymous functions do not always have names.
If you have the handle to a function but do not know the name(s) of the variable(s) that have been assigned that function handle, then you can use whos to identify the names of variables that might hold the handle, and then you can loop through the names testing with isequal() to see if they are the same handle. Note that with anonymous functions it is not enough to test whether char() of the two functions is the same, because their workspaces might be different:
a = 1;
f1 = @(x) x + a;
a = 10;
f2 = @(x) x + a;
f3 = f1;
Now strcmp(char(f1), char(f2)) would be the same, but they are not the same functions: is equal(f1, f2) will be false -- but isequal(f1, f3) would be true as they are the same function handle.
If you do take this route of searching the variables for candidates, then remember that even if the anonymous function was assigned to a variable at some point, it might have been assigned to a field or a cell array
test.f1 = @(x) x + a;
test2{1} = @(x) x + a;
so if it is important to find the name of a variable storing the function handle, you might have to search field of every variable, along with every field of every variable in an outer function this one is nested in, along with every parameter passed to this function, along with many possible properties of graphics objects, along with the timer objects, and serial objects, and udp and tcp objects, and along with the listeners, and so on.
... all of which should suggest that searching for "the" name of an anonymous function whose handle you have is probably not something you should do unless you have Very Good Reason.
