Hoe zeg ik "I'm so happy that you've learned her name." in het Nederlands?
I'd like to tell a four-year-old girl.
Ik ben zo blij dat je naam heb leren kennen.
Or even more informal (better for a 4 year old girl): Ik ben blij dat ik je naam nu ken (I'm happy I now know your name)
And
Hoe zeg ik "Had she drawn a picture? Her hands are stained with ink." in het Nederlands?
Ze heeft een tekening gemaakt. Haar handen zijn vol inktvlekken.
You could say here that her hands are "bevlekt" (=stained) but the word "bevlekt" has negative connotations as well and it would be more appropriate to say her hands are full of ink stains.
A "schilderij" is an actual painting and would imply something you would hang in a museum for example.
A "tekening" is more common for the drawings children make, even if it is made with paint.