'I didn't employ my name' vs 'I didn't use my name'

[Sonia M.]

English Error, Elementary Level

ESL/EFL Test #22 "Read before you sign", question 10

B. No, you're wrong I didn't employ my name. The car is still mine because I signed it Mickey Mouse.

(a) wrong
(b) employ
(c) mine

English Error, Elementary Level

ESL/EFL Test #22 "Read before you sign", answer 10

B. No, you're wrong I didn't use my name. The car is still mine because I signed it Mickey Mouse.

Correct entry: use
The error was: (b) employ

You have found the error but your entry is incorrect.
B. No, you're wrong I didn't employ my name. The car is still mine because I signed it Mickey Mouse.
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I am a English learner from China. I questioned about this answer. Is it a set phrase?

Many thanks!
Sonia