Asked "what day is it today?", a patient correctly answers "Tuesday." Asked next "what is your name?", she again answers "Tuesday," and continues answering "Tuesday" to several subsequent, unrelated questions before eventually giving correct answers again. Before revealing the answer: is this verbal stereotypy?

No, this is more consistent with perseveration than with verbal stereotypy. The repeated content here is specifically her own immediately preceding correct answer ("Tuesday") intruding into unrelated later questions, rather than a fixed phrase unconnected to any particular prior answer. Verbal stereotypy would instead involve the same word or phrase recurring across many different situations without this direct link to the immediately preceding correct response — the tie to the sequence of questions is what points here toward perseveration.