Most certainly ‘misleadingly high’ for the statistical reason explained in my last paragraph.
The fact that muslim parents are ‘obliged’ to choose only the one name for their male firstborn inevitably pushes that name much higher in the rankings than would be the case if those same parents had the same huge range of names to choose from as non-muslim parents: and thus gives a misleadingly high impression of the number of muslim parents unless that restriction is taken into account.
It does not matter whether the parents are ‘obliged’ or not nor do variations on the spelling of the name. The basic fact remains the same, the names are still Muslim - and that is the problem when considering birth rates in a particular country.
One day, when all these ‘obliged’ children with different spellings of Muhammed stand together in the streets to riot for Sharia Law, or kill soldiers with machetes, or whatever, it will not matter their parents were ‘obliged’ or if they spell their similar name differently. They will all be shouting “Allahua Akbar”.