Greetings of peace CuriousIncident
Firstly, it is good of you to be asking questions, as it's good to ask questions and in all good to learn about what you do not know ..
And to your question, the answer is no, Allaah SWT is the creator of the moon, therefore he is not the ancient moon god, i understand that according to some individuals who lack knowledge of islamic faith see 'ancient moon god' as something that means muslims worship the moon, this is indeed a great misconception. We do not worship the moon/creation, we worship the creator of the creation and not the creation.
Allaah - The God in arabic.
I would like to advice you to be careful where you take your knowledge from regarding Islam and it's teachings, in other words i advice you to speak to knowledgeable muslims who speak according to the Qur'aan and sunnah (sayings of the prophet Muhammad (Peace and blessings of God be unto him), and not those who have no idea what they're talking about, in case you are led to believe something which is alltogether incorrect.
I'd like to end this post with a chapter from the noble Qur'aan which is called 'Al-Ikhlaas - The Sincerety'
Say, "He is Allah , [who is] One, Allah , the Eternal Refuge. He neither begets nor is born,Nor is there to Him any equivalent." [Al Qur'aan - Al Ikhlaas]
However, If I have not answered your question completely, i hope that someone else is able to do so, and please do not hesistate to ask any more questions you may have..
.. peace ..