I believe the problem is that "push" is already a verb. So when you go to add to the object, it just uses that verb instead of creating a new one.
But you have the right idea - you want your verb to show up in the tree, in the verb list. So do it that way instead. Add the verb to the tree using the Add Verb command. Then when you go into your object, you will see that verb in the list (look at the very bottom), and you can use it directly.
This implicit creation (or not) of verbs when editing an object seems to be a never ending source of problems. It's so much better to just explicitly add the verb up front and have total control over what you're doing!