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.
There is a difference of opinion among the scholars as to whether or not the Udh-hiyah becomes due only by intention. That is, if you bought an animal with the intention to offer it as Udh-hiyah, would it become due to sacrifice it, or should you put the intention into words (in order for the Udh-hiyah to be due)? The preponderant opinion is that the Udh-hiyah will not become due unless it was designated, and that is the opinion of the majority of the scholars. According to Ar-Rawdh, with its footnotes:
They, i.e. the Udh-hiyah and hady (sacrificial animal for Hajj or 'Umrah), become due only by saying, "That (sacrificial animal) is hady or Udh-hiyah,' or, "This is (offered) to Allaah." This is because this wording entails making the action obligatory on oneself. Thus, it becomes obligatory. It also becomes due by marking or garlanding the animal with the intention (to make it hady/Udh-hiyah). But it does not become due only by intention at the time of buying or driving it. That was the opinion of Maalik and Ash-Shaafi‘i. According to Al-Wazeer, "It becomes due, in their sight, only by putting (the intention) to words because designating (an animal as a sacrifice) removes one's ownership of the animal intending thereby to draw close to Allaah. Of course, only intention is insufficient to effectuate it, like emancipation, endowment, and giving out property in charity. All these acts do not become due only by having the intention to do them."
According to Al-Insaf:
Hady and Udh-hiyah may, probably, become due only by having the intention to do so at the time of buying. That is an opinion attributed to Ahmad and the opinion of Abu Haneefah; and it was chosen by Ash-Shaykh (Ibn Taymiyyah). According to Al-Majd, "What seems from the words of Ahmad is that an animal becomes Udh-hiyah if one buys it with the intention to offer it as such, just as the hady becomes due by marking it."
Since you came to know that the preponderant opinion, Allaah willing, is that the Udh-hiyah does not become due only by the intention, it is permissible for you to keep for your family what you like thereof without sacrificing it as long as you do not utter a word that gives the impression of designating it.
Allaah Knows best.