Can We Say ‘Labbayk Ya Rasul Allah’?
Question

What is the ruling on saying “Labbayk ya Muhammad (Here I am at your service O Muhammad)” or “Labbayk ya Rasul Allah (Here I am at your service, O Messenger of Allah)”?
Praise be to Allah.With regard to someone saying “Labbayk ya Rasul Allah” during the lifetime of the Messenger of Allah (blessings and peace of Allah be upon him), there is no confusion about this being permissible. It is something that was well known among the Companions of the Messenger of Allah (blessings and peace of Allah be upon him) on many occasions. 
Al-Bukhari (128) and Muslim (32) narrated from Anas ibn Malik (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) was riding a mount with Mu`adh seated behind him, and he said: “O Mu`adh ibn Jabal.” Mu`adh said: “Labbayk ya Rasul Allah wa Sa`dayk (Here I am at your service, O Messenger of Allah).” He said: “O Mu`adh.” Mu`adh said: “Labbayk ya Rasul Allah wa Sa`dayk” – three times – he (the Prophet (blessings and peace of Allah be upon him) said: “There is no one who bears witness that none is worthy of worship but Allah, and that Muhammad is His slave and Messenger, but Allah will forbid him to the Fire.” 
Ibn Al-Anbari (may Allah have mercy on him) said: “What is meant by saying Labbayk is: I am persisting in obeying you. They used to use the related verb Labba to refer to staying in a place, and what is meant by Sa`dayk is following. Another scholar said: What is meant by Labbayk is responding time after time, and what is meant by Sa`dayk is following time after time. Al-Muhallab said: Responding by saying yes and any other word that gives the meaning of yes is sufficient, but responding to the call of a master by honouring him and saying Labbayka wa Sa`dayk is better.” (Sharh Sahih Al-Bukhari, 9/50) 
Once it is known that calling in this manner or speaking in this manner is only appropriate in the case of one who is still alive, then such a call can only be made to one who is alive and is able to hear the one who is calling him, and such words can only be addressed to one who is alive and can hear the words that are said to him. Nothing can be requested except of one who is alive and can hear, and is able to respond to the request that is made of him. 
However, what appears to be the case with regard to those who say these words and make them a slogan, and call others to it, is that they want to exaggerate in showing extreme obedience to the Messenger of Allah (blessings and peace of Allah be upon him) and adherence to his path, and to annoy those who oppose him and hate him. These are good aims that are in accordance with Islamic teachings, but this wording may give the impression – to one who does not understand the real meaning intended – that the Messenger of Allah (blessings and peace of Allah be upon him) is like any other human who is alive, and that he can hear those who call upon him or talk to him; the one who does that may move on from that to calling upon him and seeking his help, because of the wrong impression that these words may give. 
Therefore it would have been more appropriate to avoid such a slogan and to replace it with other words concerning which there is no ambiguity, especially since the true way of showing obedience to the Messenger of Allah (blessings and peace of Allah be upon him) and showing support for him, which he loved and which truly annoyed his enemies and haters, can only be by constantly obeying him and adhering to his teachings, not merely uttering claims and words. 
Shaykh Salih Al-Fawzan (may Allah preserve him) was asked: 
There are some stickers in shops on which it is written “Labbayk ya Rasul Allah”. Is this phrase permissible? Is it shirk? What should we do about it? 
He replied: 
“The word “Labbayk” is for Allah – “Labbayk Allahumma labbayk (Here I am at Your service, O Allah; here I am).” With regard to the phrase “Labbayk ya Rasul Allah”, if the Messenger of Allah (blessings and peace of Allah be upon him) were to call you (when he was still alive) and say, “O So and so,” you would say,  “Labbayk ya Rasul Allah”, as the Companions (may Allah be pleased with them) used to say when he called them. They would say: “Labbayk ya Rasul Allah.” But after his death, no one should say, “Labbayk ya Rasul Allah.” Rather you should say: “Labbayk Allahumma labbayk.”
For more details, please refer to the following answers: 72242 , 604 , 14250 , and 258503 .       
And Allah knows best.