Can I use two different cards with the same name in Commander?
No, card art or any other piece of information printed on a card doesn't matter. For card identity, the only factor is the English name being equal or not.
There are several reasons why cards with the same name can look different in print. They can be translated into another language. They can have alternate art in the same set (e.g. Hymn to Tourach). They can be reprinted in a different set, potentially with new art and/or general card style. Cards from different sets can have different printed characteristics, such as differently worded abilities, or different types (see THE GRAND CREATURE TYPE UPDATE
) due to changes in the rules or general wording conventions. Very early cards can even have misprints, such as Blue Hurricane.
However, ultimately the only factor in deciding whether or not two cards are identical is their English name; on a related note, the official characteristics of a card can be found on the Oracle website

108.1. Use the Oracle card reference when determining a card’s wording. A card’s Oracle text can be found using the Gatherer card database at Gatherer.Wizards.com.
201.2. A card’s name is always considered to be the English version of its name, regardless of printed language.
903.5b Other than basic lands, each card in a Commander deck must have a different English name.