N.H. Rev. Stat. Ann. § 518:5

If the name or residence of a party interested is unknown the notice shall be published three weeks successively, beginning at least eight weeks before the time of taking, in some newspaper printed in Concord, and in some newspaper printed in the county, and, if the deposition relate to land, a like notice shall be posted in some public place in the shire town of the county in which the land lies.