RegExp testing with ash shell (BusyBox)

You have three tools that can do regular expressions. These all assume that $in contains na-examplename-01.

1. grep

   $ printf "%s\n" "$in" | ./grep -E '^[a-z]{2,3}-[a-z]+[0-9]*-[0-9]+$'
   na-examplename-01
   

2. sed

   $ printf "%s\n" "$in" | ./sed -n '/^[a-z]\{2,3\}-[a-z]\+[0-9]*-[0-9]\+$/p'
   na-examplename-01
   

3. awk

   $ printf "%s\n" "$in" | ./awk '/^[a-z]{2,3}-[a-z]+[0-9]*-[0-9]+$/'
   na-examplename-01
   

Note that those match on each line inside $in as opposed to the content of $in as a whole. For instance, they would match on the second and third line of a $in defined as

in='whatever
xx-a-1
yy-b-2'

As Stéphane pointed out in his answer, it's a good idea to prepend these commands with LC_ALL=C to ensure that your locale does not confuse the character ranges.

awk sounds like a good candidate:

input='whatever
even spaces
and newlines
xxx-blah12-0' # should not match

input='na-examplename-01' # should match

if
  LC_ALL=C awk '
    BEGIN{
      exit(!(ARGV[1] ~ /^[a-z]{2,3}-[a-z]+[0-9]*-[0-9]+$/))
    }' "$input"
then
  echo it matches
else
  echo >&2 it does not match
fi

You could use grep in extended regex mode like this:

echo na-examplename-01 | grep -E '^[a-z]{2,3}-[a-z]+[0-9]*-[0-9]+$'

You should use the interval parameter to make this more easy to read. [a-z][a-z]|[a-z][a-z][a-z] would be [a-z]{2,3}.

[a-z]+ is the same as [a-z][a-z]*

For the grep snytax, take a look at https://www.gnu.org/software/findutils/manual/html_node/find_html/grep-regular-expression-syntax.html