All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we ask Allaah to make it easy for you to have children and bless you with righteous progeny and make them a comfort to your eyes.
Just supplicating while putting the hand on the Quran does not mean an oath or a vow. The oath that necessitates an expiation is the oath by Allaah or by one of His Names or Attributes.
Besides, a vow has certain forms, i.e. any form which implies a commitment, like ‘I vow to Allaah’, or ‘I owe to Allaah to’ or the like. As regards putting the hand on the Quran, it is a mere confirmation, so it does not lead in itself to anything.
On the other hand, if we presume that the form that you made is a vow, then it is among vowing to do permissible things (i.e. matters that do not include an act by which one gets closer to Allaah) and the majority of the scholars are of the view that such a vow does not take place and one is not required to do anything because of it. However, the Hanbali School is of the view that it takes place and the person has the choice either to fulfill it or to expiate for it.
Therefore, if you refrained from naming the child with the name which you had mentioned, and chose any other name, then you are not required to do anything but it is more appropriate to make the expiation of breaking an oath as a means of avoiding the difference of opinion among the scholars. The expiation for an oath is to free a slave or to feed or clothe ten poor people, and if one cannot do or find any of these, then he/she is obliged to fast three days as mentioned in the Quran. For more benefit, please refer to Fatwa 83652.
With regard to naming with the name Tahreem, then we have already clarified in Fatwa 82906 that it is disliked to name with any name that does not have a good meaning, among which is this name which means prohibition or prevention, and among the reasons why it is bad is that it implies difficulty and hardship, while there is easiness in making things permissible. It is for this reason that the Prophet said: "The most sinful person among the Muslims is the one who asks about something which had not been prohibited and it was prohibited because of his query." This Hadeeth was narrated by Sa’d Ibn Abi Waqqaas, may Allah be pleased with him, and reported by Al-Bukhari and Muslim .
As regards the name Yahya, it is a good name, and it was a name of a Prophet. Finally, a Muslim should choose a good name for his children, whether males or females.
Allaah Knows best.