No, you should leave it in tact as it is. The reason is that the rental has 'relationship rules' attached which simply means that you had control before, you have control now and the property does not change it's position (cost, depreciation, date placed in service, etc). The depreciation does not change regardless of how you put it in.
The date acquired does not change and the date placed in service does not change. You can rename the property and keep the date of change in your tax return notes.
@elkiandart
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