Praise be to Allah.
The majority of fuqaha’ are of the view that the one who rents something has the right to make use of it himself or to allow someone else to make use of it, because by renting it he owns the right to use it, and he may use it himself or allow someone else to use it. It is not stipulated that the owner should give permission for that. In fact, the scholars stated that if the owner stipulates the condition that only the renter may make use of it, then that condition is invalid, because it contradicts the nature of the contract, but is the contract itself valid or not?
Regarding that, there is a difference of opinion among the scholars:
The Hanafis and Hanbalis are of the view that the contract is valid, although this condition is invalid.
The Shaafa‘is are of the view that the contract itself is invalid.
It says in Kashshaaf al-Qinaa‘ (4/15): The renter himself may make use of the item or allow someone else to make use of it, by lending it to him or otherwise, because he owns the right to make use of it according to the contract. Therefore he has the right to make use of it himself or to allow someone else to do so.
If it is stipulated that only the renter may make use of it, then this condition is invalid and the renter is not obliged to adhere to it, because it is contrary to the nature of the contract, as the contract means that he has ownership of the right to use the item, and the one who has the right to use something may use it himself or his proxy may use it. End quote.
It says in Mughni al-Muhtaaj (3/474): The renter may make use of the item himself or allow someone else to do so, as it is permissible for him to sub-rent what he has rented from someone else, but it is stipulated that the one to whom he lends it must be honest.
If the owner stipulates that he should be the only one to use the rented item or property, that is not valid, just as if he sold him an item and stipulated that he could not sell it to a third party. Ibn ar-Rif‘ah suggested that this matter is subject to further discussion. End quote.
See also: Tabyeen al-Haqaa’iq (5/121); Badaa’i‘ as-Sanaa’i‘ (4/206); al-Mudawwanah (3/521); al-Mawsoo‘ah al-Fiqhiyyah (1/267).
Some of the scholars are of the view that it is valid for the owner to stipulate a condition that only the renter himself may make use of the item. al-Ba‘li said in al-Ikhtiyaaraat: It is permissible for the renter to sub-rent the rented item to someone else for the same fee that he is paying or more. This is the view of Ahmad and ash-Shaafa‘i.
But if the owner stipulates that no one is allowed to make use of the item except the renter himself, or he stipulates that he cannot sub-rent it except to a person of good character, or that he should not sub-rent it to any specific individual, Abu’l-‘Abbaas [Ibn Taymiyah] said regarding that: Based on the guidelines of the madhhab, in my view these are valid conditions, but if the renter is not able to make use of the item himself, because of sickness, loss of property, intention to travel and the like, then he has the right to cancel the contract, as is the case if the item is not usable." (Al-Fataawa al-Kubra 5/408).
The majority of fuqaha’ are of the view that this condition is invalid, because it is contrary to the nature of the contract.
As for those who regard this condition as valid, such as Shaykh al-Islam [Ibn Taymiyah], that is based on the fact that in principle, conditions are valid, even if they are contrary to the nature of the contract, provided that they are not contrary to Islamic teachings. This is a valid opinion and there is evidence to support it in the reports of the salaf. The owner may have an interest to be served in making this restriction, and if the renter accepts this condition willingly, then how can it be justifiable for him to go against it?
In the case of telecommunications companies, the issue has to do with security, lest someone uses the line to commit a crime, which will then be attributed to the one in whose name the line is.
What appears to be the case is that this is something that may be overlooked when the matter is between the father and his sons or his wife, especially since this condition is mandatory and the renter cannot reject it. So you do not have to put the line in your name.
And Allah knows best.