Yes, there are rules. You specifically ask about "methods written on arrows", so I will stick to "methods" (called "operations" in UML terms), although it is also possible to mention signals.
For methods, there are two arrow types:
- Request arrow: An arrow from caller to callee, with a solid line and a filled arrowhead (or an open arrowhead if it is an asynchronous call).
- Reply arrow: An arrow from callee to caller, at the point where the method returns, with a dashed line and an open arrowhead.
In case of a request arrow, the label of the arrow shows the name of one of the methods of the target of the arrow. In case of a reply arrow, the label shows one of the methods of the source of the arrow.
You may choose to only draw request arrows and forget about reply arrows.
The syntax of the labels of these arrows is specified in section 17.4.4 of the UML specification.
The label of a request arrow has the following syntax:

The message-name is the name of the method that is called. Example:

If you wish, you may omit the parameters and just write requestUniqueId.
The label of a reply arrow has the following syntax:

The message-name is the name of the method that just ended. Example:

You may also draw reply arrows without labels, if you don't want to show the returned values in your diagram.