26 Singers, 26 Letters
Python 2, 80 71 bytes



def f(s):i=sum(map(ord,s))%98%40;return chr(i-i/26*18+i/32*3-i/37*8+65)


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The sums of ordinals modded give numbers between 0 and 38

The numbers larger than 25 are then shifted to fill in the blanks as below (sorted sequence shown):

  0  1  2  3  4  5  6  7  8  -  -  -  - 13 14  - 16  - 18  -  -  - 22 23 24 25  - 27 28 29 30  - 32  - 34 35 36  - 38


Subtract 18 if i&gt;25:

  0  1  2  3  4  5  6  7  8  -  -  -  - 13 14  - 16  - 18  -  -  - 22 23 24 25
                          - 27 28 29 30  - 32  - 34 35 36  - 38


Add 3 if i&gt;31:

  0  1  2  3  4  5  6  7  8  -  -  -  - 13 14  - 16  - 18  -  -  - 22 23 24 25
                          - 27 28 29 30  
                                                  - 32  - 34 35 36  - 38


Subtract 8 if i&gt;37:

  0  1  2  3  4  5  6  7  8  -  -  -  - 13 14  - 16  - 18  -  -  - 22 23 24 25
                          - 27 28 29 30  
                                                  - 32  - 34 35 36  
                                            - 38


Which gives the sequence 0..25

  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


These are then converted to A-Z with chr(i+65)