Consider the following code, mostly crafted from reading the tcl wiki and documentation:

package require logger 0.3
proc log_custom_timestamp {level txt} {
  puts "[[clock format [clock seconds]]] [$level] $txt"
}

set log [logger::init main]
${log}::info "hello world"
foreach level [logger::levels] {
    interp alias {} log_custom_timestamp_$level {} log_custom_timestamp $level
    ${log}::logproc $level log_custom_timestamp_$level
}

${log}::info "hello world"

It produces the following output:

[Mon Aug 12 16:36:58 PDT 2024] [main] [info] 'hello world'
[Mon Aug 12 16:36:58 PDT 2024] [info] hello world

Observe that the original output has the logger name main, but my code does not produce the name.

Is it possible to access the logger name in logproc, so that I can customize the timestamp format while preserving the logger name?