Thank you for your post.
I am unable to replicate the issue with FileMaker Pro 13.0v4 under Mac OS X 10.10.1 and Mac OS X 10.8.5. I do not have a Mac OS X 10.9.5 available to me at this time. This is what I have done:
1. In Test.fmp12, I pulled down the File menu and select Import Records -> File...
2. I selected File.fmp12 from the Desktop, selected the "Names" table from the Source, and selected "New Table (Names)" as the Target, and clicked Import. Four records were added, and the Names layout was active.
3. I pulled down the File menu and selected Manage -> Database...
4. I clicked the "Tables" tab, selected the "Names" table, and renamed it to "TSGal". I clicked OK to exit.
5. I pulled down the File menu and selected Manage -> Layout... The TSGal table was already linked to the "Names" layout.
6. I went to Browse mode, the Names layout is active with the field data from the imported (and renamed) TSGal table.
Interestingly, I imported again from the "File.fmp12" file, this time selecting the "TESTSORT" table. After renaming the table to "Test" and immediately going to Browse mode, the layout is also automatically renamed to "Test" (not TESTSORT).
Let me know what I'm doing differently than you so I can replicate the issue.
Interesting. I did this about four times yesterday with the same results. In the end, after clearing out all tables and TOs, I started again, but this time making sure to rename the table as well as the TO and re-link the layout, and that seemed to have worked.
I will keep an eye out on this and report back with any more findings.