Steps to reproduce:
Zabbix currently supports only Oracle EZCONNECT naming.
If DBHost variable is either not defined or empty it is considered to be an error.
Please find attached a patch file for src/libs/zbxdb/db.c and frontends/php/include/db.inc.php.
If it's applied, one can erase DBHost to enable tnsnames.ora service name lookups (DBName will work as a service name in that case).