Bitcoin ATM anonymity

Would bitcoin obtained by someone who used a prepaid over-the-counter cell phone for SMS and used a pseudonym first & last name be traceable to that ATM user? If so, how? And how could anonymity be recovered.

What is the exact point with Bisq in the question ?

A fresh general paper about bitcoin+anonymity (thanks to Manfred):

These days everything is traceable if someone really wants to track you.

I am sure that it is hard to buy a cellphone without government finding out who bought it, one way or the other.

Besides, many ATMs have cameras on them or near them, so good luck staying anonymous in days of decent facial recognition software.