If you want to search a page on facebook and know the exact name then follow these steps:
1- Open facebook app in your smartphone
2- At the top bar there is a search box where you can enter your query.
3- Next you need to write down the name of searched query. For example i've searched for a page named as "Cuppycake". I enter the name in search bar.
4- After entering the name, i can see different results. Choose the one you want. Here i found my result at the first position.