@FeelTheRush , I can't remember when I saw it, but there were letters from her to her sister when she was at university, and she signed them as Hilda. It was decades ago - how she had 'become' Mrs Thatcher from being Hilda, the dowdy daughter of a Grantham grocer.
It was well-known at the time (probably 1980-ish), just as we know now about Gideon and Al. The articles were in colour supplements. Probably about a biography.
That article is quite superficial. It was quite usual in the first half of the 20th century to be named after relatives. (I'm not that old BTW)
Opting to use your middle name - as each of these party leaders did - it doesn't tell you, for example, whether Mr Wilson or Mr Brown were called James by their parents. Both had fathers called James.
At school, it was quite usual for someone to be John Name Surname, Thomas Name Surname, Margaret Name Surname, etc. with many of them known by the middle name.
I can think of several, including in my extended family. My granddad was Robert Francis Thompson, known as Bob, My uncle was something like Robert Francis Thompson, known as Robin, his son Robert Andrew Thompson known as Andy, his son, Robert Fraser Thompson, known as Fraser etc, with a few of his cousins also Robert Something Thompson.
Name styles have changed - having 2 middle names was not common, double-barrelled surnames rare, and not having a middle name unremarkable.