Can you find out who has a db open--Yes. But first some questions. Is this db entirely on your network, that means forms,queries and the tables containing your data? If so your db will crash sooner or later (leaning toward sooner). You could split the tables (data) store that on your network, call this BE (back end). Place the other parts, forms, queries, reports and any code on each individual machine, call this FE (front end). Just doing this will allow more than one person to have you db open at the same.
You will need to LINK the FE to the BE. This can be done with either the link wizard or code, both work. If both the FE and BE are always going to be in the same location use the wizard.
Now to your question, in the same folder as your db will be the ldb file. If you db is called MyData.mdb then look for MyData.ldb. Right click on this file and open with Notepad, it will give you the computer name that created this file.