The chart-topping record launched the former soldier to instant recognition in 2004, when the hit songs Goodbye My Lover and You're Beautiful were released.
He re-released it as a 20th Anniversary Edition on October 11, and promised he will change his name to what his fans decide if it tops the charts on Friday.
Blunt told ITV's Good Morning Britain that people in their "great wisdom and kindness" have chosen Blunty McBluntface - a parody of Boaty McBoatface which went viral after a campaign to find a name for the UK's polar research ship in 2016.
"The people I pity more is my family," he said.
"I feel it was stupid of me, really, to offer to change my name if you got to number one because of the consequences.
"I feel though that the British public, they will would have to live with the shame of... going out and buying and owning a James Blunt CD, (it) might be a deterrent enough."
Blunt said he is "praying" that Back To Bedlam's new edition enters the charts at number two.
He added: "I explained to my wife she would be Sofia McBluntface and she's seized on the opportunity to say she would change her name back to her maiden name (Wellesley)."
Blunt also joked that he needs to "milk this one for all it's worth on the 20th anniversary" as it is the album his fans actually bought.
The Old Harrovian and ex-member of the Household Cavalry's first album received five Grammy nominations, including song of the year for You're Beautiful and best new artist for Blunt, and two Ivor Novello Awards, including international hit of the year for the same song.
In 2022, Back To Bedlam was named the UK's second biggest debut album by the Official Charts Company.
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