** it does NOT say in Canon Law that you have to go behind a screen
So, what is the big deal?**
Your statement “he will be happy to hear your confession** unless **you do not want to be identified” is flat out wrong. THAT is the big deal.
He should be happy to hear your confession even IF you do not want to be identified.
Now the Seal of the Confessional extends not just to not revealing sins, but also to as far as possible preserve the anonymity of the penitent. Hence the requirements of Canon Law that a) confession not take place outside the confessional except for just cause and b) confessionals must be fitted with a grate or screen for anonymity.
By logical deduction, under the same requirement of preserving anonymity, a priest therefore ALSO must not ask the identity of a penitent who calls requesting confession if they indicate that they wish to remain anonymous.