Yes! If you change your BattleTag through Blizzard, all you have to do to update your Profile on HOTS Logs, is to upload a new replay with your new BattleTag in it.

Your Profile name will be updated, and all your past games will be preserved.

Note: this is related to changing your BattleTag ID on an existing account. The account is the same. If you change your BattleTag on HOTS Logs to one associated with a different account, that will not preserve your past games on the same HOTS Logs account as those are entirely different accounts, regardless of the BattleTag ID associated with it.