They actually can book a hotel room.I hope it will be different during the world cup but it isn't as simple as "do it in private" in Qatar.. people are arrested for their gender expression in public, have their phones searched and can then get detained.. and for example two men can't rent a hotel room for fear of being arrested
"In May 2022 some hotels on FIFA's official list of recommended accommodations for the World Cup event were outright refusing to provide accommodations to same-sex couples, while other hotels on the list indicated they would accept reservations for same-sex couples so long as they hid their relationship in public.[30] FIFA claimed that it would ensure that the hotels mentioned are once again made aware of the strict requirements in relation to welcoming guests in a non-discriminatory manner.[31] During a press conference in Germany on May 20, the Emir of Qatar Sheikh Tamim bin Hamad Al Thani stated that the LGBT visitors would be welcomed to the 2022 World Cup but they need to respect the nation’s culture.[32]
On 21 September 2022, According to a report by The Guardian, FA (Football Association) has assured LGBT+ couples will not face arrest while holding hands or kissing in public in Qatar. FA has also declared that fans with rainbow flags will not face arrest as long as they do not “disrespect” the local culture and norms by draping flags over mosques in Qatar.[33][3
https://en.wikipedia.org/wiki/LGBT_rights_in_Qatar"