Does an Israeli PhD grant you the right to call yourself Dr. in Germany? I am a German citizen currently studying for my master’s in Germany. I am thinking about pursuing a PhD in physics in Israel (TAU) and I am wondering if the PhD in Israel is fully equivalent to the doctorate in Germany. Will I be able to use Dr. as part of my name when I eventually return back to Germany?
I would guess possibly, but the only definite answer will come from the relevant authorities.

A quick search turns up the following results: 

https://www.anerkennung-in-deutschland.de/html/en/assessment_of_higher_education_certificates.php
https://www.auswaertiges-amt.de/en/06-anerkennungd/606684

Leading to: 
https://www.kmk.org/de/zab/central-office-for-foreign-education.html

This suggests there is a service that will assess foreign degrees regarding their equivalence for a fee.
There is also a website (in German) that will allow you to determine if your desired institution is recognised by the German state or not:
https://anabin.kmk.org/anabin.html

And lastly: You can always ask your local embassy/passport-issuing office when in doubt. They either know or can find out if the degree is recognised.

(Degrees from other EU countries are normally recognised within the EU without any additional fees.)

Edit:

Using the search of the Anabin website, "TAU" is listed as "H+".
Use the search here to find it: https://anabin.kmk.org/no_cache/filter/institutionen.html

Edit 2:
I have "two letters" in my Passport/ID card from a PhD in the UK, nowadays living in France. I did not need to pay any extra fees at the German embassy in France and my PhD Certificate from the University of Leeds was sufficient - which is also classed as "H+" in the database.