With POSIX awk:

#!/usr/bin/awk -f

BEGIN {
    print ENVIRON["AWKSCRIPT"]
}

Then:

AWKSCRIPT=test.awk ./test.awk
test.awk

I don't think this is possible as per gawk documentation:

Finally, the value of ARGV[0] (see section 7.5 Built-in Variables) varies depending upon your operating system. Some systems put awk there, some put the full pathname of awk (such as /bin/awk), and some put the name of your script ('advice'). Don't rely on the value of ARGV[0] to provide your script name.

On linux you can try using a kind of a dirty hack:

#!/usr/bin/awk -f

BEGIN { getline t < "/proc/self/cmdline"; split(t, a, "\0"); print a[3]; }

I don't know any direct way of getting the command name from within awk. With GNU awk running on GNU/Linux you can use the process ID and ps to retrieve the command name as a workaround. For example:

cmdname.awk

#!/usr/bin/gawk -f

BEGIN {
  "ps -p " PROCINFO["pid"] " -o comm=" | getline CMDNAME
  print CMDNAME
}

Output:

cmdname.awk

Using GNU awk

Checking the GNU awk user's guide - 7.5.2 Built-in Variables That Convey Information I stumbled upon:

PROCINFO #

The elements of this array provide access to information about the running awk program. The following elements (listed alphabetically) are guaranteed to be available:

PROCINFO["pid"]

The process ID of the current process.

This means that you can know the PID of the program during runtime. Then, it is a matter of using system() to look for the process with this given PID:

#!/usr/bin/gawk -f
BEGIN{ pid=PROCINFO["pid"]
       system("ps -ef | awk '$2==" pid " {print $NF}'")
}

I use ps -ef, which displays the PID on the 2nd column. Assuming the executiong is done through awk -f <script> and no other parameters, we can assume the last field of the line contains the information we want.

In case we had some parameters, we would have to parse the line differently -or, better, use some of the options of ps to print just the columns we are interested in.

Test

$ awk -f a.awk 
a.awk
$ cp a.awk hello.awk
$ awk -f hello.awk 
hello.awk

Note also that another chapter of the GNU awk user's guide tells us that ARGV is not the way to go:

1.1.4 Executable awk Programs

Finally, the value of ARGV[0] (see Built-in Variables) varies depending upon your operating system. Some systems put ‘awk’ there, some put the full pathname of awk (such as /bin/awk), and some put the name of your script (‘advice’). (d.c.) Don’t rely on the value of ARGV[0] to provide your script name.