The Safavids were the rulers of Iran, who actively used that title, operated in a Persianate cultural milieu, and used Persian as the language of administration. Yes, the native language of the Shahs was Azeri (not that it would have been called that, since an Azeri identity did not exist for a long time after), but that does not mean that the Safavid state was anything other than an Iranian one; it would be like saying Britain was a German state under George I.
Moreover, Persia is also used to represent the Afsharid, Zand and Qajar dynasties, for which the above also applies.
This is more or less exactly what I come here to post. The above is the reason the current tag is named what it is.
As long as it makes sense (which is a big if in many cases) we also employ a general preference for geographic names over dynastic or capital based ones.
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