We also say ‘Mishaneh Makom/Shem, mishaneh Mazal.’ And we do have the Mazalim. I don’t care much about the English Zodiac (except for fun), by my Mazal is a Gdi, aka. Capricorn in English. I think the Mazalim are more interesting than particularly important though.
I didn’t look it up. I learned about it in school. Mazal Teves is a Gdi, Mazal Shvat is a Dli, Mazal Adar is a Dug, etc. There are reasons certain months get certain Mazalim (my favorite is Sivan, which has the Teumim (Gemini) for the two parts of the Torah), but we didn’t talk much about it.
TPBM thinks zodiacs are fun, but not particularly important.