Are you using a PanelView Plus terminal, or running FactoryTalk View ME on a Windows XP or Windows 7 computer ?
The Trend object in FactoryTalk View ME does not log data into an exportable format; it's a binary-encoded, proprietary log file.
If you set up a "Data Log Model" then the data is logged into a log file on disk, and can be manually exported and converted into a text file. If you don't set up a "Data Log Model", then the data is cleared as soon as the Display that hosts the Trend object is closed.
There is a separate method for logging data in FactoryTalk View ME, called the DataStore Plus ActiveX control. That directly creates a log file in CSV format, and can be started and stopped programmatically so that you can go look for the data files later. The ActiveX generally puts the starting timestamp on the data file name, but does not support prompting for a filename.
These two methods for displaying data and recording data are separate. Inside FactoryTalk View ME, you won't be able to go select a DataStore log file and show it as a Trend, nor will you be able to individually save particular spans of time from a Trend as a separate log file.
Is FactoryTalk View ME your only choice for this project ? There are competitive products with much more powerful datalogging features.