There is a global variable available called @@procid (as part of the TSQL support) that may help.

Doing something along the lines of

 select proc_name from sys.sysprocedure where proc_id=@@procid;

seems to fix your purpose.

This was added back in version 5 and is still documented for V16 and still seems to work in V17. Future versions may or may not continue this tradition.

Based on Nick's suggestion, here's test code that relies on the wild guess that for triggers, the @@procid value is 0x80000000 (= 2147483648) + the trigger_id value from systrigger...

I don't think that it's documented, but it seems reasonable that code within triggers (and possibly within event handlers) will have a fitting @@procid value, too. (And it somewhat resembles the documented fact that internal connections have particular ranges for their connection numbers.)

create table T_Test
(
    pk_Test int             not null    default autoincrement primary key,
    data    varchar(255)    not null
);

create or replace proc STP_Test()
begin
    declare my_name varchar(128);
    set my_name = (select proc_name from sys.sysprocedure where proc_id = @@procid);
    waitfor delay '00:00:01';
    message 'Procedure "' || my_name || '" has proc_id ' || @@procid;
end;

create or replace trigger TIU_Test
before insert, update on T_Test
for each row
begin
    declare my_name varchar(128);
    declare trigger_proc_id_offset unsigned int = 0x80000000;
    set my_name = (select trigger_name from sys.systrigger
                   where trigger_id = @@procid - trigger_proc_id_offset);
    waitfor delay '00:00:01';
    message 'Trigger "' || my_name || '" has proc_id ' || @@procid;
    call STP_Test();
end;

create or replace trigger TD_Test
before delete on T_Test
for each row
begin
    declare my_name varchar(128);
    declare trigger_proc_id_offset unsigned int = 0x80000000;
    set my_name = (select trigger_name from sys.systrigger
                   where trigger_id = @@procid - trigger_proc_id_offset);
    waitfor delay '00:00:01';
    message 'Trigger "' || my_name || '" has proc_id ' || @@procid;
    call STP_Test();
end;

insert T_Test (data) values ('abc'), ('def'), ('geh');
delete top 1 T_Test order by pk_Test desc;
call sa_server_messages(NULL, -100);

returns the following in my test on V17.0.4.2100:

Trigger "TIU_Test" has proc_id 2147483662
Procedure "STP_Test" has proc_id 527
Trigger "TIU_Test" has proc_id 2147483662
Procedure "STP_Test" has proc_id 527
Trigger "TIU_Test" has proc_id 2147483662
Procedure "STP_Test" has proc_id 527
Trigger "TD_Test" has proc_id 2147483663
Procedure "STP_Test" has proc_id 527

Here's for events:

create or replace event EV_Test
handler
begin
    declare my_name varchar(128);
    declare event_proc_id_offset unsigned int = 0xC0000000;
    set my_name = (select event_name from sys.sysevent
                   where event_id = @@procid - event_proc_id_offset);
    waitfor delay '00:00:01';
    message 'Event "' || my_name || '" has proc_id ' || @@procid;
end;
trigger event EV_Test;

shows the following message log entry:

Event "EV_Test" has proc_id 3221225473

Each type of object (procedure, table, etc) has an object_id column in the corresponding SYS* table (e.g. sysprocedure, systable, etc). So to get the object id of an entity you need to query the associated SYS table.

For example, to find the object id of a procedure, use

select object id from sysprocedure where proc_name = 'my_procedure';

You can also just use the OBJECT_ID() function - e.g.

select object_id( 'myuser.my_procedure' );

FWIW: The OBJECT_ID() function simply queries the sysobject table to get the answer!

HTH