Naming facts exported from blocks in Isabelle/HOL
From section 1.1.2 in the document isar-ref: you can reference facts via explicit name, implicit name and literal position. In this case, the explicit name has not been provided. I believe that the canonical method to provide an explicit name is to reference the fact of interest by its implicit name immediately after the end of the block. For example,

lemma mylemma: "i = i"
proof -
  {
    fix j :: nat
    have "j = j" by auto
  }
  note name = this
  show ?thesis using name by auto
qed




As a side remark, I would like to mention that general questions about Isabelle or the syntax of Isar are best posed on Stack Overflow. I believe that this would drastically increase the chances of your questions being answered promptly.