You may open the following link where you could see the usage of the expression in question at the very outset.
“George M. Pavia, Esq. retained my services to act as trial counsel in a lawsuit against James Cyril Couri."
Kenneth V. Gomez, Esq.: George M. Pavia, Esq. retained my services to act as trial counsel in a lawsuit against James Cyril Couri.
V.
Hi,
Believe me it is perfectly correct to talk about retaining someone's services rather than retaining the person themselves. I don't see anything illogical in it, but maybe that's because it is a perfectly natural expression.
Rgds