Hi, did princes start having two names from Kosem Sultan's time? That is Suleyman and Ibrahim were originally or additionally named Orhan and Selim but Naima does not call them so, neither do these sources presented by Baki Tezcan in his article on Kosem Sultan's political debut mentioned this:
"Sâfî, who finished writing the extant version of his history in 1024/1615, mentions besides Osman, Mehmed, Selim, Murad, and Hüseyin, a prince named Hasan as well. Hasanbeyzâde and Karaçelebizâde mention three other names, Süleyman, Kasım, and Ibrahim."
This Selim could not be Kosem's son Suleyman because he was born before Murad in June 1611 but had died within weeks (Tezcan) and they were mentioned in order of seniority.
Also, Bayezid is not mentioned above so is it possible that Bayezid's other name was Hasan?
And it is confirmed that after giving birth to her third daughter Hanzade around 1610, Kosem gave birth to three sons in succession: Murad was born in July 1612, then Süleyman around 1614 and Ibrahim in November 1615?
For your first question, I can't affirm that second names for şehzades began during Kösem Sultan's time. I can affirm that Orhan and Selim were very likely the second names of Süleyman and İbrahim (as Erhan Afyoncu had proposed to Kasım and İbrahim, the former erroneously), because other seventeenth century sources refer to them with those names, and so does the letter fowarded to Venice upon Murad IV's accession to the throne.
For Mustafa Sâfî, this is what he says about those princes in "Zübdetü't-tevârîh'i": "Ve anlardan mâ 'adâ Sultân Selîm ve Sultân Murâd ve Sultân Hüseyn ve Sultân Hasan nâm şehzâdeler ki, her birinin târîh-i vilâdetleri in şâe'llâhü teâlâ mahallinde tahrir olunacakdır, vücûda gelüb, bi hamdihî teâlâ her sâl-i ferhunde-fâlde ol gülistân-ı câh u celâlden bir niçe gonça-i devlet devlet-rüste ve her dem nesîm-i se âdet ile bir gül-i gül-zâr-ı saltanat-şüküfte olmadadır."
I don't have this book at the moment to see, but it appears Sâfî didn't end up on writing that date of birth for Şehzade Hasan, if turns out I'm not mistaken. With the princes being in a seemingly order of seniority (Osman and Mehmed, if you're thinking of them, were mentioned in the same page) and Sâfî's wording, it does appear unusual that Şehzade Bayezid wasn't mentioned there, considering other contemporaries - İbrahim Peçevi Efendi, Evliya Çelebi and Mehmed bin Mehmed - all wrote that Şehzade Bayezid was younger than his half-brother Murad IV by just three months. At the same time, the prince mentioned by the Venetian bailo Simon Contarini in his relazione from 1612, who died "a year" after his birth, isn't mentioned too, only Şehzade Selim is. Şehzade Bayezid's exclusion, in that case, could be only as something Sâfî overlooked, like the other prince, and not necessarily be the same prince as Şehzade Hasan.
But as things stand, it would've been very valuable if we had a study of Ahmed I's children, to really put everything in order, as other sons could or couldn't have had second names we don't know of as well.
Such a study would've been also valuable in pointing to us the birthdates of Ahmed I's daughters. You say Hanzade Sultan is the third daughter, but we don't exactly have this information about who between Hanzade Sultan and Fatma Sultan was the older - considering their sister Ayşe Sultan is the obvious oldest daughter of Kösem Sultan and second daughter of Sultan Ahmed I. A little bit of that, I brought up on the post regarding the date of marriage of Fatma Sultan and Çatalcalı Hasan Paşa in 1628 - how the French ambassador called her "the youngest of the Sultanas" while modern historiography generally puts her among the oldest daughters of Ahmed I. It's certain though, that Kösem Sultan - who already had an older son, Şehzade Mehmed - bore three sons betwen 1612 and 1615, Murad IV, Süleyman and İbrahim.
