You could use jq:

Input file:

{
  "items" : [
    {
      "name" : "first-block-e70a2fe8fd0531ad1f87de49f03537a6",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "166219e3-be5c-46d0-b4c7-33543a29ce32"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"

    },
    {
      "name" : "second-block-c21a1ae8dd2831cd1b87de49f98274e8",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "176429e3-be5c-46d0-b4c7-33543a29ad63"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"
    },

    {
      "name" : "first-block-a85d2fe6fd0482ad1f54de49f45174a0",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "176429e3-ae1d-46d0-b4c7-66123a24fa82"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"
    }
  ]
}

command:

$ jq '.items[] | select( .name | startswith("first-block-"))|.name|ltrimstr("first-block-")' < file.json 
"e70a2fe8fd0531ad1f87de49f03537a6"
"a85d2fe6fd0482ad1f54de49f45174a0"

You could use jq:

Input file:

{
  "items" : [
    {
      "name" : "first-block-e70a2fe8fd0531ad1f87de49f03537a6",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "166219e3-be5c-46d0-b4c7-33543a29ce32"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"

    },
    {
      "name" : "second-block-c21a1ae8dd2831cd1b87de49f98274e8",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "176429e3-be5c-46d0-b4c7-33543a29ad63"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"
    },

    {
      "name" : "first-block-a85d2fe6fd0482ad1f54de49f45174a0",
      "type" : "STORE",
      "hostRef" : {
        "hostId" : "176429e3-ae1d-46d0-b4c7-66123a24fa82"
      },
      "roleState" : "STARTED",
      "healthSummary" : "GOOD"
    }
  ]
}

command:

Edit: with @Runium's contribution

$ jq '.items[] | select( .name | startswith("first-block-"))|.hostRef.hostId' < file.json 
"e70a2fe8fd0531ad1f87de49f03537a6"
"a85d2fe6fd0482ad1f54de49f45174a0"