How do I access the name of an OSC message once it has been received?

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This is what you need: a routine that uses an undocumented call in Sonic Pi which enables you to extract the actual osc message used to trigger the previous sync
I have used it over several years, together with a similar one for midi messages. (The latter had to be updated when midi messages were restructured in Sonic Pi see this post

use_osc "localhost",4560
use_debug false
use_osc_logging false

define:parse_sync_address do |address| #gets info on wild cards used in sync address
  v= get_event(address).to_s.split(",")[6]
  if v != nil
    #return a list of address elements with wild cards substituted by actual values
    return v[3..-2].split("/")
  else
    return ["error"]
  end
end

live_loop :findpushed do
  
  v = sync "/osc*/push*" #respond to button osc and save data in v[0]
  res = parse_sync_address("/osc*/push*") #use parse routing to extract actual osc message
  puts res #shows the output of parse_sync address
  puts "button ",res[1],"was triggered"
  puts "this has index",res[1][4..-1].to_i
  puts "data value sent was",v[0]
end


live_loop :test do #this loop generates osc calls from 30 virtual push buttons
  n = rrand_i(1,30)
  message = "/push"+n.to_s
  osc message,[0,1].choose #chooses random data 0 or 1 to send from push buton
  sleep 1
end

In this example I send messages from virtual push buttons named push1 to push30 with data 0 or 1 and use a single live_loop to extract the data and work out which button was activated and what data it sent.
I have used this technique very extensively especially with touchOSC interfaces.