MANILA—New hotels are sprouting across the Philippines to help fulfill the government’s ambitions to make the archipelago a match for Thailand or Malaysia as a top Asian holiday destination. Now the challenge is to fill them.

The hotel boom—including upscale foreign brands like Shangri-La and Hyatt—is designed to address a perennial shortage of accommodation that, along with poor transport links, officials say has long stunted tourism in the country.

But...