The Hebrew word "shem" is translated into the English "name" but, just like the English word, it does not always mean "a personal indicator of identity" or something like that. We use the word "name" to indicate a title or a rank, or even a characteristic or excellence (he made a name for himself as an electrician). In this case, God is known by his attribute of being zealous (the word "kana" isn't simple human jealousy. Here
is an explanation from about 1000 years ago:
"קנא שמו WHOSE NAME IS קנא — Who is zealous (מקנא) to exact punishment from the sinners and is not indulgent towards idolatry. This (the above) is always the meaning of the root קנא wherever it is used in connection with God. Consequently קנא שמו His name (His characteristic) is קַנָּא that of a zealot, implies: He maintains (insists upon) his superiority over other gods, and punishes His enemies (those who worship idols)."