I have just purchased a MOTO E3 and transferred my BT Mobile Sim to it. Before it was showing BT as the network provider now it shows it as EE. I know that BT mobile is piggy-backed on EE but I am concerned by the change.
Aslo when making calls, just before it connects the message "conditional forwarding on call" flashes up.
Showing BT / EE is normal, phones display the name of the mast by the MNO if the MVNO hasn't got its name assigned to said mast, hence how on EE you'll sometimes find it still says Orange or T Mobile in some places - so nothing to worry about on that one - you can see the following link that talks about HLR settings on your pofile, if it is bothering you just give BT a ring and ask for a HLR profile refresh, once complete you will need to restart your handset, HLR refreshes are generally 'finalised' in about 30 minutes, and you may need to redo your APN settings on your handset afterwards / network reset on your handset. https://community.ee.co.uk/t5/Archive/Phone-showing-Tmobile-orange/td-p/41108
As for Conditional Call Forwarding - open up your Phone app, hit the menu button (should look like 3 dots in the corner), go to Call Forwarding and disable all the options (should be tick boxes), then save or just back out of the menus if there is no save option .