Specifying the name of the person on whose behalf the sacrifice is being offered
Question

Do I have to slaughter the hadiy (sacrificial animal) myself or is it permissible to appoint one of the companies or banks in Makkah that specialise in that (to do it on my behalf)?
Praise be to Allah.The individual is not obliged to slaughter his hadiy himself; it is permissible to appoint a trustworthy person to do that on his behalf. However it is important to note something that has to do with appointing or delegating someone to do that on one’s behalf, which is that at the time of slaughter, it is essential to state the name of the one on whose behalf it is being done. So the one who is doing the actual slaughter should intend that it is on behalf of So and so; it is not permissible to slaughter a number of sheep, for example, on behalf of a number of people without stating the names with each slaughter. 
Based on that, it is not permissible to appoint companies or banks that do not specify the names of the people on whose behalf the sacrifice is being offered, except in the case of necessity, when it is not possible for the individual to go to the slaughter place himself or to find a trustworthy person to slaughter the sacrifice on his behalf. 
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: Some Hajj groups collect money from the pilgrims for the hadiy (sacrifice), and they slaughter the animals on their behalf, but they may fail to mention the name of the one on whose behalf the sacrifice is offered at the time of slaughtering each animal. Is this permissible? 
He replied: This is not permissible. It is essential to state on whose behalf this sacrifice is being offered every time an animal is slaughtered. For example, if there are thirty men in the group, and he (the person who is offering the sacrifice on their behalf) buys thirty sheep for them, he should have a list of their names in front of him, and every time he brings a sheep forward (for slaughter), he should say: “This is on behalf of So and so,” because it is essential to state on whose behalf it is being offered. If he just sacrifices thirty sheep on behalf of thirty men, that is not valid. 
End quote from al-Liqa’ ash-Shahri, 73/32 
He (may Allah have mercy on him) was also asked: We have heard that you warned people against giving money to these companies, but what is the solution with regard to what has happened in the past? We did Hajj more than once, and we gave money to these companies and they did not take our names. What is the ruling on what was done in the past? Is it acceptable? If it is not acceptable, what do we have to do? 
Answer: We did not warn against giving the hadiy (sacrifice), because in fact the hadiy is necessary. The individual has two choices: either to give money to these companies or to sacrifice it himself and leave it on the ground, in which case neither he nor anyone else will benefit from it. If the person is able to slaughter his hadiy and eat from it, give some of it as a gift and give some of it in charity, then undoubtedly this is much better. This is possible for some people who have acquaintances in Makkah and are able to delegate them to do this on their behalf, telling them: Slaughter the hadiy on our behalf. In that case he can benefit from it, or he can go to Makkah, go to the slaughterhouse and buy an animal and slaughter it there, and he will find people crowding around him to take it from him. But what I think is a serious mistake is to send the cost of the sacrifice to another country so that it can be sacrificed there. This is the thing for which there is no basis. The Prophet (blessings and peace of Allah be upon him) used to send the sacrificial animal to Makkah to be sacrificed in Makkah. There is no report from him, either in a saheeh (sound) or da‘eef (weak) hadeeth, that suggests that he sent his sacrificial animal (udhiyah) to any other place; rather he used to slaughter it in his house, and they would eat from it, give some of it as gifts and give some as charity.
End quote from al-Liqa’ ash-Shahri, 34/17 
If the company writes down the name of the person on whose behalf the sacrifice is being offered, and hangs it around the sheep’s neck, as some companies do, and the slaughterer forms the intention that this sacrifice is on behalf of the person whose name is written on this paper, then that is acceptable and valid. It fulfils the need to specify on whose behalf the sacrifice is being offered, and it is not necessary to mention the person’s name after that. 
And Allah knows best.