I just want to ask that what will happens if we applied the same license on different nodes of distributes environment. Like I was installed a splunk enterprise license on License Manager that is now working as a search head. But the same license of LM installed on another search head or indexer of the same environment. Then what will happens regarding to it?
It's easy: you hare in violation!
You cannot use the same license on different Indexers,
Probably you haven't any message if your infrastructure isn't connected to Internet and your LMs are in different and not connected networks, but it's a violation.
As @gcusello said that is license violations. Usually you should have only one LM where licenses are. Then you can create one ore more pools to divide those between nodes. If needed you can add secondary LM for test/dev environment if you don't want to share same pass4SymmKey between prod and dev/test. BUT never use the same license file on several LM or directly on nodes. If needed you could ask that Splunk Support splits your license to smaller chunks (separate lic files) and use those to different LM nodes. You could move those freely between LM when needed. One hints rename lic files as some reasonable name like 5gb-xyz-2023-06.lic 5gb-yxx-2023-06.lic. That way it's easier to recognise than looking GUIDs 😞
Usually indexers/SHs recognise if there are same license in use on several nodes and give you a notice. If you don't fix the situation then your searches stopped after 72h, if I recall right what this notice said.