Beata was a common name in Germany. Its origin is Latin and means "blessed" as in beatify or beatification.
Phil

The Beateah entered the familiy when William's father -William BRAIN married Beateah BEDDIS , and they had a daughter Beteah in 1822( ish)

WILLIAM BRAIN was born Apr 1785 in Little Dean, Gloucestershire, England, and died 24 Jun 1849 in East Dean, Gloucestershire, England. He married BEATEAH BEDDIS daughter of JAMES BEDDIS and MARY MEREDITH. She was born Apr 1775, and died 3 Dec 1859 in Edgehills, East Dean, Gloucesteshire, England

Children of WILLIAM BRAIN and BEATEAH BEDDIS are:
i. JAMES BRAIN, b. 10 Jun 1807, Little Dean, Gloucestershire, England; d. 24 Aug 1886, Collafield, Gloucestershire, England.
ii. WILLIAM BRAIN, b. 1807
iii. BENJAMIN BRAIN, b. 1809
iv. CHARLES BRAIN, b. 1811
v. ELIZABETH BRAIN, b. 1813
vi. THOMAS BRAIN, b. 1817
vii. BETEAH BRAIN, b. 1822
viii. EMILAH BRAIN, b. 1824
ix. LUCY BRAIN, b. 1828

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Year: 1834
Month: Jan
Day: 12
Parents_Surname: BRAIN
Child_Forenames: Beata
Fathers_Forenames: William
Mothers_Forenames: Sophia
Mothers_Surname:
Residence: Edge hills
Occupation: Labourer
Officiating_Minister: H. Berkin
Event: Baptism
Memoranda:
Notes:
Register_Reference: P109 IN 1/1
Page_Number: 135
Parish_Chapel: Drybrook

1881 ( with other Brain / Grindle and Hale families)
William Brain abt 1801 Littledean Head Westbury On Severn - East Dean Gloucestershire
Beatias Brain abt 1836 Collafield Daughter Westbury On Severn - East Dean Gloucestershire

1891

Westbury on Severn Workhouse

Beta Brain abt 1832 Littledean, Gloucestershire, England Pauper Westbury On Severn, Gloucestershire

Name: Beta Brain
Estimated birth year: abt 1832
Year of Registration: 1894
Quarter of Registration: Jan-Feb-Mar
Age at Death: 62
District: Westbury On Severn
County: Gloucestershire
Volume: 6a
Page: 187

Year: 1894
Month: Jan
Day: 31
Surname: BRAIN
Forenames: Beta
Residence: Westbury Union
Age_at_death: 62
Officiating_Minister: J. H. N. Barton Curate
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: P85/1 IN 1/14
Page_No: 32
Parish_Chapel: Cinderford St Johns

First name origin & meaning:

Latin: Blessed

First name variations: Beatta, Beeta, Beetah, Beita, Beitah, Beyta, Beytah, Beata

A little off track from the origional question of where Beta might have been in 1871 I know, but intriqued by the workhouse connection prompted me to visit to Gloucester Archives.

Beata's time in the workhouse is documented through out the Westbury Union statement of accounts for the years 1883 (half year to Michaelmus) to 1894 (half year to Lady Day) - found within the east Dean list of Indoor Paupers. So as you see it seems she reamined here for around 11 years,until her death.

The weekly cost of maintence per head in 1893 is noted as
including necessaries. s. d.
2 7 1/2
weekly cost of clothing 0 7 1/4

total cost 3 2 3/4

It is not clear why she entered the workhouse from these records, however it seems her father William may have been receiving outdoor relief from the parish for some of this time due to being infirm. (1888-1895)

ref 1888 Westbury Union statement of accounts through to 1895 (half year ending Michalmus)

It would apprear from these records that he was approx aged 78 when he died and was infirm, listed as living in either The Ruffet or Collamore.

Another small piece to the jigsaw!