The chart-topping record launched the former soldier to instant recognition in 2004 when hit songs Goodbye My Lover and You're Beautiful were released.
He re-released it as a 20th anniversary edition on Friday, and promised he would change his name to what his fans decide should it tops the charts once more.
Blunt said people in their "great wisdom and kindness" have chosen Blunty McBluntface, a parody of Boaty McBoatface which went viral after a campaign to name the UK's polar research ship in 2016.
"The people I pity more is my family," he told ITV's Good Morning Britain.
"I feel it was stupid of me, really, to offer to change my name if you got to No.1 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 No.2.
"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)," he added.
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 first album by Blunt, a former member of the British Army's Household Cavalry, earned five Grammy nominations including best new artist and song of the year for You're Beautiful, and two Ivor Novello songwriting awards in the UK, 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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