Praise be to Allah.
One of the things that is recommended with regard to naming children is to give the child names of Prophets and Messengers, and the best of Prophets’ names is the name of our Prophet, Muhammad (blessings and peace of Allah be upon him).
Shaykh Bakr ibn ‘Abdullah Abu Zayd (may Allah have mercy on him) said: The sixth principle: names in order of preference in terms of how recommended or permissible they are.
Children may be named after the Prophets and Messengers of Allah, because they are the leaders of the sons of Adam, their characters are the noblest of characters, and their deeds are the purest of deeds. So giving their names is a reminder of them and of their characteristics and stories. The scholars are unanimously agreed that it is permissible to give their names to our children.
The best of Prophets’ names are the names of our Prophet and Messenger, Muhammad ibn ‘Abdullah (blessings and peace of Allah be upon him and all his fellow Prophets and Messengers).
End quote from Tasmiyat al-Mawlood, p. 15-16
Based on that, it is better to leave your son’s name as it is; praise be to Allah, it is a good name.
With regard to what you mentioned about the child not being able to distinguish the name Muhammad, this is a problem that will quickly pass as the child grows older, and it will not have any negative impact on him at all, in sha Allah. People still call their sons by this good name, in the East and in the West, among Arabs and non-Arabs, and they do not find any problem with that or any difficulties for their children.
May Allah make things easy for you and bless your offspring.
And Allah knows best.