It is possible to change the format of Time ID. From inside the project select, Project > Forecasting Settings. This will open the "Forecasting Settings" dialog. A screenshot is also attached for help.
In the "Forecasting Settings" dialog select the "Time ID" card on the left hand side. This will show you all the settings related to Time ID. There is "Format" field and associated Edit button, click on the Edit button which will bring up "Edit Time ID Format" dialog. Choose the "Select from list" radio button. You can select various types of time ID formats including MONYY which you are looking for.
Press OK in all dialogs to save your choice. Once you are back to project, you will be able to see the format on every view of Forecast Server. Let me know if it helps.
Regarding the data truncation issue, the forecasts begin after the last non missing date for the dependent variable and it is same for the whole project. Need to check the last date against the dependent variable. If you still see the issue can you share the data with me?
Regards,