Besides getting a new customer?
It takes work. No matter what, anyone who dumps data over the wall without explanation is going to find a way to slip something past.
The way I have handled such a thing is via structures and groups. I make the overall updated assembly structures the same as the previous one and then group components in the new version based on the old one. This finds the items that are new, and finds items that are omitted. The groups are set such as a plate is grouped with the fasteners that hold the plate in place; nuts, bolts, washers. If I can see 8 holes and 8 nuts, 8 bolts, and 8 washers all in proximity of the holes in the plate, I am very sure this is correct. It also cuts down on stupid things. Example. I've seen cases where a ref-pattern fails. Since the user didn't bother to group the fasteners with the item, it looks at a glance, like only one fastener is present. So they manually assemble replacements into the holes. End result - 8 fasteners in one hole, and 7 new fasteners for a total of 15. Not cool.Interference checks could find this, but the fasteners get flagged for interfering with the nuts, so unless one is counting carefully, that won't help (and failing to count carefully is how it got this way to begin with.)
A quick run at a mass-properties report should find noticeable shape changes, though it's possible for mutually cancelling changes to be made, I find it unlikely they will be a perfect match. This should find all items where shape dimensions changed. It won't find cases such as shifted holes; changes that can't affect the volume.
If you haven't got a PDM system, I would create a search path and create separate folders for the various versions, searching the latest one first and working back. You can do this in advance and create as many empty folders as exceeds your expectation for revisions. Then put the newest work you do in the associated folder so you can tell at what point you had to make a change to accommodate their revision. I would not rename with a suffix; I would probably rename what they sent, to match what they sent before; keep a spreadsheet of those name changes. It shouldn't matter much as you always have their STEP file to verify what their name for the item was in any version they sent. I think the rename is recorded in the part history.
Try to get an inside contact with the customer. Someone should be keeping track of what is changing and why. I've been burned before by too many intermediate layers of people who have no idea how CAD/CAE works and assume it is as complicated as Notepad.
