Dynamic changing column in sql statement, where more if conditions? PostgreSQL

I am trying to have a dynamic variable that I can specify different column's with (depending on some if statements). Explained in code, I am trying to replace this:

IF (TG_TABLE_NAME='this') THEN INSERT INTO table1 (name_id) VALUES id.NEW END IF;
IF (TG_TABLE_NAME='that') THEN INSERT INTO table1 (lastname_id) VALUES id.NEW END IF;
IF (TG_TABLE_NAME='another') THEN INSERT INTO table1 (age_id) VALUES id.NEW END IF;

With this:

DECLARE
varName COLUMN;
BEGIN
IF (TG_TABLE_NAME='this') THEN varName = 'name_id'; 
ELSE IF (TG_TABLE_NAME='that') THEN varName = 'lastname_id'; 
ELSE (TG_TABLE_NAME='another') THEN varName = 'age_id';
END IF;

INSERT INTO table1 (varName) VALUES id.NEW;
END;

The INSERT string is just an example, it's actually something longer. I am a beginner at pgSQL.. I've seen some examples but I'm only getting more confused. If you can provide an answer that is also more safe from SQL that would be awesome.