No, as Haramain is conducting thousands of Qurbanis for individuals around the world, this is practically not possible. It is also not necessary to give the name of the person, even if you are making a Qurbani on behalf of someone else. As long as you have made the intention that you are giving this Qurbani on behalf of a certain person that should be sufficient.
It is advisable to give the money as early as possible. The time for offering the sacrifice during the Eid Period begins after the Eid prayer on Eid al-Adha and ends when the sun sets on the 13th of Dhu’l-Hijjah. So there are four days of sacrifice: the day of Eid al-Adha and the three days after it.
Since Qurbani is an act of worship, then one has to offer the best. Therefore, Haramain adopts a high-quality standard when it comes to selecting the sacrificial animals. The standards cover health, weight, and age. Also, we would like our brothers and sisters to receive the best quality Qurbanis because the believer is asked to love for his brother/sister that which he/she loves for him/herself.
It would be better if individuals did not visit, as on the day the Haramain on the ground are extremely busy with slaughtering the animals. Therefore, the Haramain will not have the capacity or time to host individuals except in the case of Hajj group leaders.