Hiram was orphaned as a child, so I wonder if he had mis-heard "Logan" and inadvertently changed his middle name to "Morgan" (or if his foster/adoptive parents made the error).
Did Sarah deliberately change her middle name from Alice to Althea?  Did she get the idea from Althea HUNTER?  Or is the 1870 census in error? 

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

Samuel A. HILL Spouse: Julia Ann SLOANE Marriage: 10 Jun 1847, Cape Girardeau, Missouri Source: Marriage Records, 1805-1950. Cape Girardeau County (Missouri). Recorder of Deeds

Hirum Morgan HILL Birth: 1848, prob. North Carolina Father: Samuel Allen HILL (1820-1854); Mother: Julia Anne SLOAN (1828-1853) Source: patron submission

2.  1850 Census Every-Name-Index/Images (online at Ancestry.com, Image #15-16 of 292 — middle initial indexed "N"):  District No. 14, Cape Girardeau Co., MO, Roll 394 (Book 1), pp. 348A-348B, 100/101, enumerated 10 Aug 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):

Samuel A Hill	30	M		Lawyer	2500	Mo
[next page]
Julia Hill	20	F				Mo
Sloan  "	3	M				"
S A    "	4/12	F				"
George F Taucher	35	M		None		Germany

Also living in Cape Girardeau are Samuel's parents (q.v.) and Julia's father, Hiram L. SLOAN (æ 49, b. NC; p. 343A).

3.  1860 Census Every-Name-Index/Images (online at Ancestry.com, Image #56 of 88):  New Madrid P.O., New Madrid Co., MO, Roll M653_636, p. , PN 66, 453/453, enumerated 13 Jul 1860, official enumeration date 1 Jun 1860 (extracted by Diana Gale Matthiesen):

Isaac Hunter	39	M		Farmer	22060	19000	Mo
Ellen    Do	27	F					"
Atha     Do	14	F					"
Molly    Do	8	F					"
Amanda   Do	7	F					"
Abraham  Do	5	M					"
Franklin Do	1	M					"
Jackson Hill	14	M					"
Hiram    Do	13	M					"
Sally    Do	9	F					"

Isaac HUNTER's first wife was Susan HILL.  No doubt Samuel HILL and Susan HILL were related, but the 1840 census shows no daughter (of any age) in Samuel's parents' household, which casts doubt on them being siblings.  Who is Jackson HILL?  I can't find him in 1850.

4.  1870 Census Every-Name-Index/Images (online at Ancestry.com, Image #50 of 134):  Hotel, Cape Girardeau City (Ward 1), Cape Girardeau Co., MO, Roll M593_765, p. 88B, PN 8, 56/52, enumerated 1 Aug 1850, official enumeration date 1 Jun 1870 (extracted by Diana Gale Matthiesen):

Hill Alice	20	F	W	No Occupation			Mo
____ Morgan H	23	M	W	"			Mo

They are two of 15 guests in the hotel.

5.  1880 Census Every-Name-Index/Images (online at Ancestry.com, Image #23 of 28):  Baldwin Hotel, Market Street, City and County of San Francisco, CA, Roll T9-0075, p. 260C, PN 23, SD 1, ED 83, enumerated 10 Jun 1880, official enumeration date 1 Jun 1880 (extracted by Diana Gale Matthiesen):

1880:  for an explanation of the column headings, please see What the Numbers in the Federal Census Mean (missing columns contained no data).
	1	2	3	4	5	6	8	9	13	24	25	26
*	84	104	Hill Morgan	W	M	30	Boarder	/	Fancy Goods	MO	MD	MD
			____ S A	W	F	27	Boarder	/	At home	MO	MD	MD
*Market

Both have shaved three years off their age.  They are two of many guests in the hotel.

6.  Missouri History: Missouri State Legislators, 1820-2000 (online at the Missouri State Secretary of State web site):

Name	Party	Office	County	Elected
Hill, Samuel A.		Rep.	Gape Girardeau	1846,50

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

8.  Beth Wyman.  1983.  Hiram Morgan Hill.  Self-published.