Basic thoughts
The basic situation has already been clarified by the previous answers. I would like to add that the first word order that comes to mind is:
Ich gebe Herrn Müller das Buch.
This can emphasise, the object, but usually not strongly. There are certainly other permissible word orders. The first one would be:
Ich gebe das Buch Herrn Müller.
which normally emphasises the recipient. Of course verbal stress plays a role. Then there is a case for contrasting recipients. What they receive also gets stressed, albeit less:
Herrn Müller gebe ich das Buch, Nina die Gitarre!
Naturally, there are cases where stress becomes a major aspect:
Das Buch gebe ich Herrn Müller, das Geld aber Nina.
Das Buch gebe ich Herrn Müller, alle anderen aber Nina!
About es
Usually – there are exceptions – when we use es, it receives very little emphasis and often only serves grammatical correctness. Hence, we pick an order not emphasising it:
Ich gebe es Herrn Müller.
Proper nouns
Having pondered for a few minutes, I can’t discern anything special about proper nouns:
Ich gebe dem Hund den Knochen.
Ich gebe ihn dem Hund.
Ich gebe Herrn Müller das Buch.
Ich gebe es Herrn Müller.
About zu
In this sense, adding zu is not permitted. Adding zu often invokes significant changes:
Ich gebe es zur Reparatur. – I gave it away for repair.
Sie gab das Mädchen zu den Nonnen. – She gave the girl to the convent (probably for education)
Ich gebe Salz zur Suppe. – I add salt to the soup.
About the last example, I am not sure if it is idiomatic. I tend to express it differently.
So if we correct your example, adding an n, it may occur, albeit in a very different sense from what you probably thought. For instance, we may have:
Ich habe ein kleines Mädchen. Ich gebe es für ein halbes Jahr zu Herrn Müller nach London, damit es Englisch lernt!