How to display information of person who booked room on Outlook Calendar?

This is controlled by the permissions on the Calendar folder. Namely, the user will need to have "LimitedDetails" or equivalent permission in order to be able to see this information. If you want to ensure that all users in the tenant will be able to see it, you can use the following:

Set-MailboxFolderPermission -Identity RoomName -User Default -AccessRights LimitedDetails

And if you want to configure this on all rooms, use this:

$calendars = Get-Mailbox -RecipientTypeDetails RoomMailbox | Get-MailboxFolderStatistics -FolderScope Calendar | ? {$_.FolderType -eq "Calendar"} | select @{n="Identity"; e={$_.Identity.ToString().Replace("\",":\")}}
$calendars | % {Set-MailboxFolderPermission -Identity $_.Identity -User Default -AccessRights LimitedDetails}