Typos aside, it is your understanding of the name change which does not tally. It is the name for the O/S which is being changed. Demo:

#!/usr/bin/perl 
use strict;
use warnings;

print "I am $0 (@{[join ' ', @ARGV]})\n";
system ("ps $$");
shift;
exit unless @ARGV;
my @args = ('bar', 'foo.pl', @ARGV);
system { '/usr/bin/perl' } @args;
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Running this I see:

$ ./foo.pl 1 1
I am ./foo.pl (1 1)
  PID TTY      STAT   TIME COMMAND
 3717 pts/0    SN+    0:00 /usr/bin/perl ./foo.pl 1 1
I am foo.pl (1)
  PID TTY      STAT   TIME COMMAND
 3719 pts/0    SN+    0:00 bar foo.pl 1
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So the name in the O/S has changed to 'bar' but within the script, $0 is still foo.pl since that is the file which perl is executing. Additionally, if you call system ('./foo.pl') the O/S uses the hashbang line to re-exec perl with the script as argument (as in the initial invocation in my run above), so your aliasing there would have no effect even at the O/S level.

say $0;
$0 = 'python';
say $0;
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($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
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You didn't close your use statement on line 2 of bar

#!/usr/bin/perl -w
use strict;
__________^
system { './foo' } 'bar', @ARGV;
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Which fixed it for me. :-)

EDIT:
Didn't -w scream at you?

that was probably due to my editing the post to remove some unwanted noise (ie. hostname, username etc.) >> Which fixed it for me. :-) you meant it actually printed out "I am bar (1 2 3)" as expected? (ie. $0 gets 'bar' instead of './foo') . what perl version did you use? i've tried this on all 5.16, 5.18 and 5.22 ... all the same. thanks for looking at it.

Having only added the semicolon to the bar script. My copies were exactly as you posted them.

Just for fun. Here's the output from my session:

devel# ./bar
Can't exec "./foo": No such file or directory at ./bar line 3.
Unknown 'strict' tag(s) '-1' at ./bar line 3.
BEGIN failed--compilation aborted at ./bar line 3.

devel#
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Ahh, sure enough. No semicolon on line 2 -- gotta love that -w :-)

devel# ./bar
I am ./foo ()
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Looks good. Lets try it as intended

devel# ./bar 123
I am ./foo (123)

devel#
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I think I can safely reply now. :-)

Evil is good, for without it, Good would have no value
¡λɐp ʇɑəɹ⅁ ɐ əʌɐɥ puɐ ʻꜱdləɥ ꜱᴉɥʇ ədoH

The OS can't lie to perl as to which script to execute because Perl wouldn't be able to find the right script to execute, and $0 contains the name of the script passed to perl, so $0 must necessarily contains the correct name of the script.