How to open a file with a dynamic name using VBA?

Question

Visual Basic

It was not possible to collect a working answer in Google.
I have a macro that processes a file with the current date in the title:

Dim my_file As Worksheet
Set my_file = Workbooks.Open(Filename:=ThisWorkbook.Path & "\important file" & Date & ".xlsx").Sheets(1)
'do anything
Workbooks("important file" & Date & ".xlsx").Close SaveChanges:=False

How can a file be opened with any character set instead of Date? And if you get .xls?

Answer 1

- read a list of files from a folder
- check if the beginning of the file name matches "important file"
- process the files from the received list with your macro in turn, if there are several of them

Answer 2

Do you mean it will fall? Where do these files come from? Or do you randomly take the name of the file and try to open it?
Explain a little more please.