A good deal of confusion about our subject's "surname" has resulted from the failure to distinguish between his patronymic (Larsen) and his efternavn (DOMGAARD), and the same problem applies to his children.  Because DOMGAARD was not a "true" surname, it could be dropped at any time in preference to the patronymic because to a Dane (prior to the mid-19th Century) the patronymic was the more important name.  However, if you want to be consistent about his name (and when using computerized databases, this is a must), his full name would be the one I've used above, and only DOMGAARD should be considered a surname.  To more clearly distinguish between patronymics and surnames, I recommend always putting the former in Initial Caps, while always placing the latter in ALL-CAPPS.  Please see this discussion of patroymics and this one on Danish naming practices.

Lars and Lauritz are Danish variations of the Latin name, Laurentius.  Laurtz is a misspelling (apparently someone dropped the "i" and the error has been repeated ever since).

— born in Hals, Hals Sogn, Kær Herred, Aalborg Amt, DK:
3.  Johanne Larsen DOMGAARD, b. 22 Sep 1838; d. 22 Dec 1928, St. Anthony, Fremont Co., ID
4.  Anceselie / Ane Cicilia Larsine Larsen DOMGAARD b. 20 Sep 1840
5.  Stine Petrine Frances Marie Larsen DOMGAARD, b. 5 Apr 1843
6.  Lauritz Larsen DOMGAARD, b. 9 Mar 1846; d. 21 Jun 1848
7.  Lauritz Larsen DOMGAARD, b. 2 Aug 1850

The source for the Ulsted location is secondary, so may not be accurate.  Stine is said to have been born in Longesminde, but I can find no such place, at least not officially.  Like Domgaard, it may be a very local name or farm name.

Some secondary sources show Elizabeth as having married Jens (James) HANSEN (JENSEN), and some show Johanne as having married him, each on 9 Nov 1854 in Salt Lake City.  It may very well have been a polygamous marriage with both sisters marrying the same man on the same day (I've seen other such cases among Mormons), or it may be that two men are being mixed up here, as the name certainly suggests.  That is, that the husbands are Jens HANSEN and James JENSEN and they married sisters on the same day in a "double wedding" (a wide-spread custom).

Anceselie and Ane Cicilia (both born in 1840) are surely the same person; the two given names must simply have been run together (as when Mary Ann becomes Maryann).

1.  1834 Census of Denmark (online at Dansk Demografisk Database):  Lars Christian Domgaard is shown as age 30, an unmarried laborer (tjenestekarl) living with the KYLLESBECH family, along with about a dozen others in what appears to be a boardinghouse in "aalborg, Kær, Hals, Hals by."

2.  LDS.  Family Search: Internet Genealogy Service:  IGI - International Genealogical Index (online at FamilySearch.org).

Lars Christian Doomgard Birth: 19 Sep 1802, Hals, Denmark; Death: 05 Oct 1854 Spouse: Metta Christina Christiansen Birth: 04 Feb 1812, Ulster, Denmark Source: patron submission

Lars Christian Larsen or Domgaard Christening: 19 Sep 1802, Hals, Aalborg, Denmark; Death: 04 Oct 1854 Father: Lars Christensen or Domgaard; Mother: Elizabeth Larsen Marriage: 01 Jun 1834, Hals, Aalborg, Denmark Spouse: Mette Kirstine Christensen Birth: 04 Feb 1812, Ulsted, Aalborg, Denmark Father: Christen Christensen; Mother: Maran Anderrsen Source: patron submission

Lars or Laurtz DOMGAARD LARSEN Birth: 19 Sep 1802, Hals, Aalborg, Denmark; Death: 04 Oct 1852 Father: Anders NIELSEN KJAERSGAARD; Mother: Ane NIELSEN Marriage: 01 Jun 1834, Hals, Aalborg, Denmark Spouse: Mette Kristine CHRISTENSEN Source: patron submission

3.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org).

.  Edmund West, comp. 2000.  Family Data Collection.  MyFamily.com, Inc., Provo, UT (online at Ancestry.com; n.b., West is an undocumented secondary source):

Name:	Lars Larsen	Lars Domgaard	Elizabeth Domgaard	Johanne Domgaard	Johanne Larson	Stine Larsen
Date of Birth:			2 Nov 1834	22 Sep 1838	22 Sep 1838	5 Apr 1843
Place of Birth:			Ulsted, Aalborg, Denmark	Hals, Aalborg, Denmark	Hals, Aalborg, Denmark	Longesminde, Hals, Denmark
Name of Father:			Lars Larsen	Lars Larsen	Lars Domgaard	Lars Domgaard
Name of Mother:			Mette Kristine Christensen	Mette Kristine Christensen	Mette Kristine Christensen	Mette Kristine Christensen
Date of Marriage:	1 Jun 1834	1 Jun 1834
Place of Marriage:	Hals, Aalborg	Hals, Aalborg
Name of Spouse:	Mette Kristine Christensen	Mette Kristine Christensen

I can find no such place as "Longesminde."  Was it the name of a farm?

4.  1850 Census Every-Name-Index/Images (online at Ancestry.com):  can't find.

5.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).