Yes they do but not all of them.
Wammy's House is one of several orphanages established by Watari (real name Quillsh Wammy) after World War II, initially a training facility for especially gifted children. After it's most accomplished child, L Lawliet (AKA L) become a renowned detective the goal of Wammy's House chnaged to produce a successor to L.
The orphans use aliases rather than real names and notable graduates are assigned letters. in L: Change the WorLd and email i sent out after Watari's and L's death with the mailing list filled with letters, a number of them are grayed out and assumed dead because Beyond Bithday who is given the Letter B, is too on the list but grayed out
As for how the Letters are assigned it seems that it is based off the first letter of their Alias as while L, Nate and Mihael start with their assigned letters, Quillsh Wammy is Watari and has the letter W. Beyond Birthday is also known as Rue Ryuzaki though this may not be his real name as he was pretending to be L for a period. A is mentioned in Death Note: Another Note however we don't know if A was also is alias like with L or even his real name
you can read up on on the Characters related to Wammy's House however it should be noted that the information is from L: Change the WorLd, i am unsure which one the information is from as K is in the Movie but the Novel is more faithful to the canon bu al;tering the plot of the movie.