Hi,
Out of curiosity: what prompted the question?
First of all, your sentences are perfectly intelligible. I would change two three things:
1. (Added) In your original, the pen is undefined, but in your translation it's defined. That's not not wrong per se, but if you want an exact rendering and not "the pen", then it's "un pix".
2. The structure of the dative in Romanian includes a "doubled" pronoun:
I-am dat un pix lui Mark.
3. The noun has a dative form:
Masculine: I-am dat un pix copilului.
Feminine: I-am dat un pix mamei.
In the case of proper nouns, we don't use a dative form for boy names (we add "lui" instead) but we do modify girls' names if they end in "-a".
I-am dat pix lui Mark.
I-am dat un pix Taniei.
However, if the girl name ends in something other than -a, or is a foreign name, we can safely revert to the pattern used for the masculine
I-am dat un pix lui Carmen.
I-am dat un pix lui Tanya/Tanyei (I'd use whichever).
I hope that makes some sense. :/
Edited because I missed some info.