Is there a website for the UK like the social security site in the USA for keeping statistics on baby name popularity?

Depends on what part of the Uk. Here in NI the Northern Ireland Statistics and Research Agency (NISRA) publishes an annual list of not only the most Popular names but also the names of all children born each year and how common the name was. I imagine that Scotland, Wales and England each have their own records. I used this when naming my own children- I picked simple names but ones that hadn’t been used by any other children in the previous few years.

https://www.ons.gov.uk/peoplepopulationandcommunit...

Also, why does almost every Muslim name their kid "Muhamamad?". They can't make images of him, not even stick figures, but they'll overuse his name.

This might help - https://www.ons.gov.uk/visualisations/dvc363/babyi...