What is the ruling on naming a newborn after a shaykh who has performed miracles, and will the children bear the burden of that?

All praise is due to Allah, and may peace and blessings be upon the Messenger of Allah, his family, and his Companions. To proceed:

Your grandmother's visit to this person varies depending on his condition:

If he is a righteous man who supplicates for her to have a child, then there is no harm in that.

However, if he is a sorcerer, a soothsayer, or a charlatan, then it is not permissible to go to him.

In either case, naming the child after this person is not problematic, as long as the name itself is not forbidden. If it is forbidden, then it should be changed, following the example of the Prophet (peace and blessings be upon him), who changed ugly names.

And Allah knows best.