Praise be to Allah.
Firstly:
In the answer to question no. 1692, we have listed names that are mustahabb, makrooh and haraam.
Secondly:
It is not prescribed to call the baby Adhaan, because the Adhaan comes under the heading of words and phrases that point to the Oneness of the Creator, may He be glorified and exalted. So it refers to an act of worship and one of the manifest symbols of Islam, like salaah (prayer) and Hajj. Based on that, it is not prescribed to give this name to the baby.
The meaning that you referred to in your question is correct, which is that this name may lead to things that are not acceptable according to sharee‘ah.
It should be noted that naming the child is the right of the father, not the mother, but nevertheless he should consult the mother concerning this matter and give consideration to her wishes, so that this will not be a cause of disputes and divisions.
What is required is to choose a good name for the baby.
And Allah knows best.
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