So I did some digging and found what may be a good solution for your request via an undocumented REST API call.
Basically what the call does is pull a history of your imports for that import activity.
GET /automation/v1/imports/{{importActivityID}}/history
Host: {{subDomain}}.rest.marketingcloudapis.com
Authorization: Bearer {{auth_token}}
Content-Type: application/json
It defaults to 50 records per page, but via the $page and $pageSize parameters you can increase this. something like appending ?$page=1&$pageSize=200
to the endpoint.
The return on this call is something like:
{
"page": 1,
"pageSize": 200,
"count": 62,
"items": [
{
"importFileTransferHistoryId": 0,
"filename": "myFile_20210714.csv",
"importSucceeded": true,
"importStatusMessage": "Completed",
"importStatusDescription": "OK",
"transferType": 0,
"activityType": 1,
"attempts": 1,
"transferSucceeded": true,
"importFileStatus": "1",
"startDate": "2021-07-14T01:35:04.813",
"totalRecordsCount": 29200058,
"totalRecordsImported": 29200058,
"totalRecordsSkipped": 0,
"totalRecordsDuplicates": 0
},
{
"importFileTransferHistoryId": 0,
"filename": "myFile_20210711.csv",
"importSucceeded": true,
"importStatusMessage": "Completed",
"importStatusDescription": "OK",
"transferType": 0,
"activityType": 1,
"attempts": 1,
"transferSucceeded": true,
"importFileStatus": "1",
"startDate": "2021-07-11T01:30:06.197",
"totalRecordsCount": 29122249,
"totalRecordsImported": 29122249,
"totalRecordsSkipped": 0,
"totalRecordsDuplicates": 0
},
{
"importFileTransferHistoryId": 0,
"filename": "myFile_20210710.csv",
"importSucceeded": true,
"importStatusMessage": "Completed",
"importStatusDescription": "OK",
"transferType": 0,
"activityType": 1,
"attempts": 1,
"transferSucceeded": true,
"importFileStatus": "1",
"startDate": "2021-07-10T01:49:00.963",
"totalRecordsCount": 29077130,
"totalRecordsImported": 29077130,
"totalRecordsSkipped": 0,
"totalRecordsDuplicates": 0
}
}
Which should give you the fully rendered file name that you are looking for.
A caveat to this though is that it only returns the past 60 days of records - so anything beyond that would be lost.
This also brings the note of it being an undocumented endpoint so its use at your own risk as it is not officially supported by SF. This means at any moment it could be turned off, changed or otherwise adjusted. It also may not be designed for heavy frequency or volume of calls, which can cause the endpoint to slow down or fail.