From Designer, you can move a service from one folder to another and the alias will stay with the service.

From Integration Server, when you use the Integration Server package replication feature to copy a package from one Integration Server to another, any HTTP URL aliases associated with the package stay with it. This is true whether the alias was created from Integration Server or from Designer or Developer.

When you receive a package from another Integration Server, it is possible that an alias associated with the new package has the same name as an HTTP URL alias already defined on your Integration Server.

Integration Server maintains a registry of HTTP URL alias names, and displays the contents of this list on the Settings > HTTP URL Alias screen. Integration Server builds this list when it loads packages during server startup, and when an alias is added, edited, or deleted. In cases where two packages are associated with the same alias name, Integration Server uses the alias associated with the first of the two packages to load. When the second package is loaded, Integration Server flags its associated alias as a duplicate, and does not add it to the registry.

In other words, Integration Server uses package load order to determine precedence. WmRoot is always loaded first. The order in which other packages are loaded depends on other factors, such as package dependencies and operating system, and therefore cannot be easily predicted.

For this reason, when you install a package that was published by another Integration Server, check the details screen for the package (Packages > Management > package_name) for load warnings.