Family tradition is that her name was Mary Ann but census records seem to suggest that her name was probably Mary Jane.

1850 Census, District 76, Reynolds Co MO (family 136)

Name Age
Zacariah Rowe 20 m OH
Jane Rowe 20 f NJ
Richard Rowe 1 m MO

1860 Census, Jersey Co IL

Name Age
Z P Rowe 30 m OH
Mary J Rowe 30 f NJ
Richard Rowe 11 m MO
Ganthy Rowe 10 f MO
Sarah E Rowe 5 f KS
Zacha M Rowe 3 m KS
Mary A Rowe 7.12 f IL

1870 Census, Farmington, Republic Co KS

Name Age
Zachariah P Rowe 40 M W OH
Mary T Rowe 40 F W NJ
Richard L Rowe 21 M W MO
Sarah Rowe 14 F W KS
Zachariah Rowe 12 M W KS
Mary Rowe 7 F W IL
Iuicy Rowe 5 F W IL
Clara Rowe 2 F W KS
Alice Rowe 1 F W KS

1880 Census, Spring Creek, Greenwood Co KS

Name Age
Zacharia Rowe 50 W M OH OH VA
Mary J. Rowe 50 W F NJ NJ NJ
Lucy E. Rowe 18 W F IL OH NJ
Clara B. Rowe 13 W F KS OH NJ
Alice Rowe 11 W F KS OH NJ
Maggie Rowe 9 W F KS OH NJ
Henrietta Rowe 6 W F KS OH NJ
Quintilda Rowe 4 W F KS OH NJ
Matilda Rowe 4 W F KS OH NJ

1900 Census, Bolton, Cowley Co KS

Name Age
Y P Rowe 70 W M Jan 1830 m52 OH OH VA
Mary Rowe 70 W F Feb 1830 m52 NJ NJ NJ

There are 5 Rowe families listed in Ross Co OH in 1840:

William Rowe: 1 m 50-60; 1 f 50-60.
Anzismer (Auzimus) Rowe: 2 m 5-9; 1 m 10-14; 2 m 15-19; 1 m 20-29; 1 m 30-39; 1 f 30-39.
Elijah Rowe: 1 m <5; 1 m 20-29; 2 f <5, 1 f 10-14; 1 f 20-19.
James Rowe: 1 m 5-9; 1 m 15-19; 1 m 20-29; 1 m 30-39; 2 f <5; 1 f 10-14; 1 f 15-19; 1 f 30-39.
Mary Rowe: 1 m 10-14; 2 m 20-29; 2 f 5-9; 2 f 10-14; 1 f 40-49.

Zachariah Poindexter Rowe would have been 10 at the time of this census, so if he and his family lived in Ross Co OH as of the 1840 census, this wold mean he could have been son of Anzismer Rowe or of Mary Rowe, but there is no male aged 10 in the other three families.