newsavebox named after counter

The following will create saveboxes \MyStringa to \MyStringz:

\makeatletter
\count@=0
\loop\ifnum\count@<26
  \advance\count@\@ne
  \expandafter\newsavebox\csname MyString\@alph\count@\endcsname
\repeat
\makeatother

It's also simple (even simpler) with expl3:

\usepackage{expl3}

\ExplSyntaxOn

% loop from 1 to 26, #1 denotes the current value in the cycle
\int_step_inline:nn { 26 }
 {
  \exp_args:Nc \newsavebox { MyString \int_to_alph:n { #1 } }
 }

\ExplSyntaxOff

With \exp_args:Nc we jump over \newsavebox and form a control sequence token from the braced argument before \newsavebox is actually performed.

In the log file we'll find something like

\MyStringa=\box46
\MyStringb=\box47
\MyStringc=\box48
[...similar lines...]
\MyStringy=\box70
\MyStringz=\box71

confirming that the allocations have been performed.