It should be this: I work at the front desk of a hotel. a hotel - the speaker declines to state exactly which hotel. the front desk - The assumption is that there is only one front desk in that hotel, so you know which front desk of that hotel is being referred to.
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bassaI work at the front desk of Double Tree hotel. Do we need to put "the" before Double?I would put "the", but you don't have to. It's OK without "the".
bassaI work at the front desk at Double Tree.OK.