Well, if anyone is interested, I've learned a lot about Anveo, and how this feature works in particular.
First of all, my problems were due to the OBi DigitMap for for "Service Providers ITSP profile for Anveo. The original setting (don't know where it came from) which I posted in my first post blocked a lot of required information. Evidently, OBi needs to know when a number is complete to send it, so it was sending it early, and telling Anveo to use CallerID 01, quickdial entry 1 if I sent *011, or quickdial entry 2 for *012, etc. With no quickdial entries, it gave a busy signal. This feature might be useful to some, but not really to me.
Changing the DigitMap to "(*xx.|1xxxxxxxxxx|<1925>[2-9]xxxxxx|<1>[2-9]xxxxxxxxx|011xx.|xx.|(Mipd)|[^*]@@.)" fixed all the problems, although if I wanted to dial something like just *012, there will be a 10 second delay before OBi decides I'm done.
This custom callerID page only chooses the outgoing number, not the name. In fact, possibly in response to my confustion, they changed the "Name" column to "Title", to emphasize that the name entered is not a callerID name (CNAM), but just a label for the entry to identify it for future use.
The custom callerID is mostly useful for setting up address book entries, I think. For each person in the address book, you can enter a custom callerID number, and this is where the "Title" is useful. I have not confirmed whether this is automatically used when you dial out, but I would like to assume it is.
So, it was frustrating, but useful in that I learned a lot about the OBi configuration and the Anveo website and configuration. It's not so bad once you learn your way around, and their incoming IVR is very good. I was able to quickly set up a call flow where people not on my contact list need to press 1 to continue, or 2 to leave a message (actually any other key for now), and get disconnected if they don't do anything.
If they are on a blocked list, they get sent immediately to voicemail, or a different blacklist can give them a number disconnected message (or hang up/give busy signal). This is all really easy to do graphically once you get the hang of it.