敬語N4
申す
to say (humble)
Structure
申す（言う の謙譲語）
Explanation
The humble form of 言う for one's own speech (私は田中と申します), commonly used in self-introductions.
Examples
私は田中と申します。
My name is Tanaka.
改めてお礼を申します。
I'd like to thank you again.
Note
申す is the humble of 言う; と申します is the standard humble self-introduction. Slightly less formal than 申し上げる.