I don’t think it’s your sort of thing but [name_m]Broderick[/name_m] would work as a way to get to [name_m]Beck[/name_m].
While not intuitive I could see [name_m]Baxter[/name_m] called [name_m]Beck[/name_m] working perhaps for close friends and family.
[name_m]Booker[/name_m] could work? [name_m]You[/name_m] wouldn’t shorten to Book so [name_m]Beck[/name_m] makes sense as an alternative.
There’s also surnames or town names that would probably work but don’t seem your style, such as:
[name_f]Berkeley[/name_f]
Beckford
[name_f]Bexley[/name_f]
Colbeck
[name_m]Beacon[/name_m]