There is no way to rename fields via a script. But field names need not be visible on any layout save table views on your layout so why is it important to change the field names?
Sounds like you have used field names where you need additional text fields that serve as labels for your fields. Such could be renamed by a script.
Yes, on the layout they won't see the field names, I could easily just change all of the labels and it would look fine. However, if they ever went to edit the layout, which I don't necessarily have to give them access to but would rather have them be able to fiddle with their layouts without having to contact us and have us do it for them every time, they would be able to see the field names which don't match their company, which I feel would look unprofessional. Thanks though, I didn't think see a way to do it either, it would be nice if you could though!
Sounds like you have field names that "match a company" that shouldn't match any company.
I would be very careful about letting your clients modify layout designs. It creates at least two major issues for you:
1) Scripts in FileMaker are, on average, very "layout sensitive". Seemingly simple changes to a layout design can easily cause scripts to fail and the only way that you can tell that this happened is when the script fails to produce the expected results--which could be catastrophic for your client's data.
2) The client initiated changes mean that their file is now different from any copy you have in your possession. This can create a number of issues should they want you to later make changes in your database design--especially if they do not have a good backup system in place to create and keep multiple backup copies on hand.