This sense of **_mark_** (to _take note of_ ) is found here¹:
5. Notice or pay careful attention to.
_‘he'll leave you, you mark my words!’_
It doesn’t look like it’s intended to refer to a name, just a simple word play (you could just about get away with using _spot_ instead, since that also has meanings which include _notice_ and _stain_ ).
¹ Oxford _Living_ Dictionaries