In her caption for the video, Ebony wrote: "She was called KAREN".
The video has since gone viral on TikTok.
Ebony went on to explain that her baby was initially going to be called Arthur but she ended up changing her mind about the name.
In a follow up video answering viewers' questions, she said: "At first, we decided on the name Arthur ... there was no boy name we were totally in love with ... and then we both agreed that we liked Arthur".
"Not long after, I decided that I didn't really like it. It's a nice name, but I wanted something a bit more unique. Something that not many people are called," she added.
Ebony already had a boy named Beau and said she never planned on giving her sons such similar names.
"I never intended to have matching baby names, the whole both of them starting with a B was not something that I did plan on.
"Then I saw Bleu on a baby app or something and it's exactly how I felt when I'd first seen Beau.
"When I'd first seen the name Bleu I was like, 'that's a bit of a weird name ... like that's a bit silly', but then I couldn't stop thinking about it, I fell in love with it and I liked it a lot better than I did Arthur."
The new mum clarified that is pronounced Blue, like he colour blue, but "spelled the French way".
The video received dozens of comments in support of the mum’s choice.