Well I don't write procedural code, and haven't for a long time... probably about 3-4 years by now.
My code nowadays uses namespaces in php, and all my autoloading is done based on namespaces too, so I don't need require/include statements all over the place either...
I guess to do this in a procedural way, I'd probably have some kind of dbConnect() function, that would take a constant as a parameter... The constant would point to some config file (like a yaml or xml file) that would contain the database connection details. The script would then create the database connection based on those details.
So for example, if I wanted to connect to two different databases, I could do $connectionA = dbConnect(DATABASE_A);, and for the other I could do $connectionB = dbConnect(DATABASE_B);
If I needed to change the password settings or whatever, I'd change it in the mapping file. There'd be a direct connection between a parameter in the mapping file and the constant value (so it'd be like: DATABASE_B = 'report_database' and then in the yaml file or whatever, there'd be a 'report_database' key).
Does that make sense?
I'd probably do something like that...