Yes, it is absolutely fine to stay at any hotel across India with anyone you like. There is no law that prohibits you from doing so. However, the law does stand against criminal activities that one might undertake during his or her stay at a hotel, in which case, as a responsible management, any hotel may inform the authorities/police.
Further, any hotel has the complete right to deny admission to whomsoever they wish to, for any reason. Many hotels will not allow unmarried couples to stay at their hotel simply in order to save their image from being defame and police harassment, and not because there is any law against unmarried couples that they can’t stay together in a hotel room. Any low budget hotel allowing unmarried couples to stay is bound to attract attention and is prone to support prostitution, an illegal activity, which may invite occasional police raids, an unwanted scenario for the hotels and the guests. However, this is generally the case with low budget hotels only. Luxury Hotels (or premium hotels) do not bother with such issues and the police interference is minimal. However, they'll generally require acceptable photo ID cards for each individual above 18 years of age. In case you do not submit the same, they may again deny admission.
And again if you are staying at a premium hotel registered with LuvStay then I want to assure you that you don’t have to face such unwanted scenarios as we want to make things easier, comfortable, pleasant and hassle free for you.