More formal:
* Payagan: This is a more direct translation of "allow" and is widely used.
* Pahintulutan: This is the more formal form of "pahintulan" and emphasizes permission or authorization.
* Bigyan ng pahintulot: This means "to give permission."
More informal:
* Pwede: This means "can" and is used for granting permission in everyday situations.
* Okay lang: This literally means "it's okay" and is used for casual permission.
The best synonym for "pahintulan" will depend on the context and the tone you want to convey.