Rule 707.11 · Copying Objects

If an effect refers to a permanent by name, the effect still tracks that permanent even if it changes names or becomes a copy of something else.

Example: An Unstable Shapeshifter copies an Olivia Voldaren. Olivia Voldaren reads, “{1}{R}: Olivia Voldaren deals 1 damage to another target creature. That creature becomes a Vampire in addition to its other types. Put a +1/+1 counter on Olivia Voldaren.” If this ability of the Shapeshifter is activated, the Shapeshifter will deal 1 damage and you will put a +1/+1 counter on it, even if it’s no longer a copy of Olivia Voldaren at that time.