The number that you see in Connect is assigned by Connect and is not stored in the file. When you download the file from Garmin Connect the file name will be 4651015926.fit. That might be where FIT Files Tools is getting the name from. When I use FIT file tools the name of the file is fitfiletools.fit, which is different than what you are seeing. So make sure you are looking at the correct file. Inside of the FIT file there is a serial number in the FileId message, but that is not the same number that is shown in Connect. I used the FIT to CSV tool to convert a FIT file to csv then searched the CSV file. I did not find the number that Connect is showing.
Ben