This article states that Mohammed is number 1 because...
The name, when 12 different spellings were included...
The other article states...
Mohammed ranked 16th nationally for boys...
The Daily Telegraph probably didn't run the search using all permutations of Mohammed. Now...did the Daily Mail use all permutations of Tom, Dick and Harry? Probably not. I suspect the Daily Telegraph did likewise.
I didn't do Tom, Dick and Harry - but I did do James, Charles, Henry, William, and John.
Daily Mail reports 7,449 'Mohammeds' (counting all the variant spellings). They are actually wrong on that - they missed one vairant, so the real count is 7,552.
If we look at all the variants of John (such as Jon), we find 11,598.
William (variants include Wiliam), we find 8,959.
Henry (Henri as an example), 8,389.
James (Jaymes), 9,689.
All four of these come in above Mohammed.
Charles (Charls) comes in slightly behind at 7,081.
I guessed at five common English names - and when we compare all variants as was done for Mohammed, four of the five come in ahead of it.
Took me about two hours to do this - it's certainly not beyond the resources of a newspaper to do it, if they want the facts, rather than a good headline.