The trivial solution is to put those newlines where you want them.
var="a
b
c"
Yes, that's an assignment wrapped over multiple lines.
However, you will need to double-quote the value when interpolating it, otherwise the shell will split it on whitespace, effectively turning each newline into a single space (and also expand any wildcards).
echo "$p"
Generally, you should double-quote all variable interpolations unless you specifically desire the behavior described above.