You've observed a very real phenomenon; it sounds like you just haven't learned the name for it yet.
I'm wondering what if my language puts every preposition before the
I give my pen to him. → I togive my pen him.
(The two objects should be distinguished by dative / accusative case,
but there's no such thing in English.)
is called an applicative construction.
The applicative is an example of a "valency-increasing operation" - similar to the causative, and opposite to the passive - that you do to a verb to promote an oblique object to a direct object. ("Oblique" in this context is a catch-all term basically for anything that isn't the subject or direct object.) In German, since direct objects are marked by the accusative case, this means the applicative would be a modification you make to verbs that take a dative or genitive object, and transforms that verb into a verb that takes an accusative object.
Applicatives are probably most famous in Bantu languages like Swahili, but they're common worldwide. WALS' survey implies that ~45% of the world's languages have a morphologized applicative construction - although their methodology is kind of wonky; the sample size is only 183 (for comparison, the object-verb word order survey has a sample size of over 1500) and doesn't count English and German even though both arguably do have an applicative.
Your particular example of *"I togive my pen him." is a little awkward though in that it has two direct objects simultaneously. You promoted the oblique object "to him" to the direct object "him" - good - but then you also kept the old direct object "my pen". Not all languages with an applicative necessarily allow that - they might require you to delete the existing direct object, or else relegate it to an oblique role. But some languages, called double-object languages, don't distinguish direct vs. indirect objects in ditransitives anyway - they're all just "objects" - so for them, the applicative really is equivalent to just slapping an extra object onto the verb.
If we go back to WALS and combine the maps for 109B (Other Roles of Applied Objects) and 105A (Ditransitive Constructions: The Verb 'give'), you get this map. With "Legend" in the top left corner, we can filter for just the languages that have an applicative construction (a value of anything other than "No applicative construction" in the first column) and double object marking in ditransitives ("Double-object construction" or "Mixed" in the second column), and we find that e.g. Swahili and Indonesian would theoretically allow something like your example sentence. I speak neither so I can't really personally confirm that though.