I believe your goal is as follows.
- You want to know whether the values of a range of "A2:B2" is moved.
In this case, how about using the named range, OnChange trigger, and PropertiesService? I thought that when those are used, your goal might be able to be achieved. When the sample script is prepared, it becomes as follows.
Usage:
1. Create a named range.
As a sample, please create a named range to the cells "A2:B2" as "sampleNamedRange1". Ref
2. Prepare sample script.
Please copy and paste the following script to the script editor of Spreadsheet. And, please install OnChange trigger to the function installedOnChange.
function installedOnChange(e) {
var originalRange = "A2:B2";
var nameOfNamedRange = "sampleNamedRange1";
if (!["INSERT_ROW", "REMOVE_ROW"].includes(e.changeType)) return;
var p = PropertiesService.getScriptProperties();
var pv = p.getProperty("range");
if (!pv) pv = originalRange;
var range = e.source.getRangeByName(nameOfNamedRange);
var a1Notation = range.getA1Notation();
if (a1Notation != pv) {
p.setProperty("range", a1Notation);
Browser.msgBox(`Range was changed from ${pv} to "${a1Notation}". Original range is "${originalRange}".`);
}
// var values = range.getValues(); // The values are not changed because of the named range.
}
3. Testing.
In this case, please do I added a row under A1:B1. By this, the script is automatically run by the OnChange trigger. And, you can see the dialog. You can see the demonstration as shown in the following image.

Note:
- This is a simple sample script. So, please modify this for your actual situation.
References:
Added:
From the discussions, I understood that you wanted to retrieve the named range of the specific sheet using the name of the named range. In this case, the sample script is as follows.
When the sheet name is used
const range = SpreadsheetApp.getActive().getSheetByName("sheetName").getRange("nameOfNamedRange");
or
const range = SpreadsheetApp.getActive().getSheetByName("sheetName").getNamedRanges().find(n => n.getName() == "nameOfNamedRange").getRange();
When the active sheet is used
const range = SpreadsheetApp.getActiveSheet().getRange("nameOfNamedRange");
or
const range = SpreadsheetApp.getActiveSheet().getNamedRanges().find(n => n.getName() == "nameOfNamedRange").getRange();