Could have a different syntax and grammar, like Της Λιζ της αρέσει ... or "αρέσει της Λιζ να μαγειρεύει ..." but also "αρέσει στη Λιζ ... ". Greek chaos. But not "H Λιζ αρέσει ..." or "Τη Λιζ αρέσει ...".
We've all struggled with this learning Greek. Sotos and Perseas have explained it well.
It took me a while to realise αρέσει doesn't mean like as we English use it. It means to please, as in "to cook/cooking pleases Liz". Liz is the indirect object - so της + της or στη Λιζ. The same construction is used in French and German.
You can even use it other than in the third person! Μου αρέσεις = you please me/I like you! At least with the pronoun coming before the verb in Greek the I and you are in the same order as in English, even if they are used differently.