If you've made aliyah, you surely know the term for ID card - תְּעוּדַת זֶהוּת (teh-oo-DAHT zeh-HOOT). The root of זהות - identity - is ז.ה.ה (z.h.h).
To identity with someone or something is לְהִזְדָּהוֹת (leh-heez-dah-HOHT). For example, הוּא מִזְדָּהֶה עִם הָעָם הַיְּהוּדִי (hoo meez-dah-HEH eem hah-AHM hah-yeh-hoo-DEE) - he identifies with the Jewish people. Today, on the Fourth of July, I also proudly מזדהה with the American people - as an American.
Or, a woman might say to her friend, אֲנִי מִזְדָּהָה עִם מָה שֶׁאַתְּ אוֹמֶרֶת (ah-NEE meez-dah-HAH eem mah sheh-AHT oh-MEH-ret) - I identify with what you're saying.
The word להזדהות falls into the intensive-reflexive form - the הִתְפָּעֵל (heet-pah-EHL). So, in theory, the word should be לְהִתְזָהוֹת (leh-heet-zah-HOHT). However, since that's difficult to pronounce, the t and z sounds switch, and the t takes on a voice to blend well with the z, thus becoming a d.
Try pronouncing the variations - this may help you make sense of that last sentence in the previous paragraph.
In the meantime, listen and repeat...
I'm going to take a few moments over the next day to reflect on my הִזְדַּהוּת (heez-dah-HOOT) - identificaion - with the Jewish people. Specifically, I'm going to reflect on what I do have in common with Jews who are unlike me - religiously, politically, ethnically...
Then I'm going to take a few moments להזדהות with human beings from all walks of life.
I invite you to do the same.