The name visible under an Android icon is intended for people. Technical identifiers serve a different purpose. Confusing the two can make support reports and package comparisons less reliable.

Start with the visible identity
Record the app's full displayed name and its official publisher listing. That is enough for many ordinary support questions. Similar names do not establish that two packages belong to the same publisher, so include the source rather than only a screenshot of an icon.
Use technical identifiers when relevant
A package or application identifier can help distinguish apps that share a display name. Obtain it through trusted app information or documented developer tooling when the task requires it. Do not infer an identifier from a filename supplied by an unknown download site.
Keep signing in the picture
An identifier alone does not establish an authorized update relationship. Android signing rules matter as well. A copied name or identifier should not be treated as proof that a third-party package can safely replace an existing installation.
Improve the report
When asking for help, provide the official listing, version and exact error. Include a technical identifier if you have verified it and it clarifies the issue. Avoid turning a routine support task into a manual package replacement unless the developer specifically provides a supported process.