A rental contract gives the renter possession of the item for a set, or perhaps indeterminate period in return for a fee, often paid in timely instalments.
At the termination of the contract, the item is returned to the owner. The owner does not lose ownership.
A call contract is completely different.
If you own shares and sell a call contract over them, you are not renting your shares out, you are selling the "right to buy" your shares. This confers an obligation on your part to sell your shares if the contract buyer exercises their right.
The call buyer never takes possession of your shares unless he/she exercises the right to buy and effects a transfer of ownership.
Selling options is more akin to selling insurance and has nothing to do with renting.
If you want to look like a nooooob and a muppet, use the term share renting. If not, use the proper terminology.