Sender name in "send HTML mail" rule
Try this variation of your rule (using the rules UI to import it in your site):

{ "rules_entityform_client_confirmation_email_pv" : {
"LABEL" : "Entityform Client Confirmation Email PV",
"PLUGIN" : "rule",
"OWNER" : "rules",
"TAGS" : [ "entity_rules_entityform_submission" ],
"REQUIRES" : [ "rules", "mimemail" ],
"USES VARIABLES" : {
  "entity" : { "label" : "Entity", "type" : "entityform" },
  "continue" : { "label" : "Continue Rules", "type" : "boolean" }
},
"IF" : [
  { "user_has_role" : { "account" : [ "entity:user" ], "roles" : { "value" : { "4" : "4" } } } }
],
"DO" : [
  { "drupal_message" : { "message" : "Email to: [entity:user:mail]\r\nHi [entity:user],\r\nThanks for creating a new project\r\n" } },
  { "mimemail" : {
      "USING" : {
        "key" : [ "entity:entityform-id" ],
        "to" : [ "entity:user:mail" ],
        "from_name" : "[site:name]",
        "from_mail" : "somebody@example.com",
        "subject" : "New Project Created",
        "body" : "Hi [entity:user],\r\nThanks for creating a new project",
        "plaintext" : "Hi [entity:user],\r\nThanks for creating a new project",
        "language" : [ "" ]
      },
      "PROVIDE" : { "send_status" : { "send_status" : "Send status" } }
    }
  }
],
"PROVIDES VARIABLES" : [ "continue" ]
}
}


The only difference with your exported rule is the line with from_mail that is added (and a slightly different machine name of your rule). Adapt the eMail Id I used to fit your needs.