@Molly: I strongly advise against giving run-time created objects a name because then it is in your responsibility to make sure that the name is unique.
If thou are unable to create unique name/numbers using Pascal then thou are not worthy of dynamic programming ;-)
You have a point but, please also do not exaggerate the negativity of it. e.g. dumping a load of components on your form at design-time is simply the same thing, and by magic the designer is able to come up with unique names.
I already stated that (at least for me) using component names or not for dynamic components depends on the situation.
I would even be bolder and state the opposite: How dare you create components without a (unique) name, so that you are unable to (uniquely) identify them other than by their address (and what happens if for some reason you lost that address).
As howardpc already noted the name is useless at run-time, maybe only for debugging. If you need one of these objects you can access it using its variable name.
Or i can search for it using the application variable. That way i am able to access a component from another form, without the need to clutter things creating a specific (global) variable for it.
If the point of the majority that oppose to naming dynamically created components is to not burden a newbie, then i am able to see a point, otherwise and so far i have great difficulty with the arguments that are expressed against it.