Can either end of a Rope of Climbing be commanded to attach - or just the end opposite to what you are holding?
If you hold one end of the rope and use an action to speak the Command Word, the rope animates. As a Bonus Action, you can Command the other end to move toward a destination you choose...You can also tell the rope to fasten itself securely to an object or to unfasten itself, to knot or unknot itself, or to coil itself for carrying.
After animated - can you let go of the rope after it is animated or do you have to hold it the whole time? Even if you have to hold it to command it - could you command either end to fasten to something? (Thus ensuring a “magically” secure attachment at both ends.)
Addendum: After reading the answers below - it raises the question whether a PC can grab one end of the rope - tell it to fasten to them - then grab that fastened end and tell the other end to go fasten elsewhere - thus giving a “secure” attachment at both ends. This would likely depend upon whether a DM rules you can “hold” the end of a fastened rope.