Faithen,
I can see the Hannah whose birth was registered in Newcastle Registration District in the Dec Qtr of 1893. Source FreeBMD site.
On the same site, I cannot see a Hannah Rose registered in Newcastle in 1897 ! What was your source for this birth or birth registration ? More on this later.
On Census 1901 , in 65 Sycamore St, Elswick, Newcastle ( page ref 4768-139-12) there is William and Hannah with a son John W aged 11 yrs and a dtr Hannah aged 7 yrs, born Newcastle.
On C1891 the family is in same house with Agnes 16, Mary, 9 amd James Wm, 1 ( page ref 4194-71-45)
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You mentioned " Gloucester Terrace/Place". Gloucester Terrace is/was in the same area of Elswick as was Sycamore St..
Using FreeBMD to see ( but not to mention) the names of children that a Bilton/Rose couple registered from 1914 to about 1927, ... shows some commonality with the first names of the above Rose family. See for yourself !
( It was interesting to see another Bilton/Rose couple registering children in the York Reg District from 1922 to 1928... James F Bilton married Edith Rose in York Reg Dist in March Qtr 1922)
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Back to beginning, it looks possible/probable that the Hannah who married Ralph was the Hannah who was registered in 1893 in Newcastle .
However it is not certain !
Assuming for the moment that there was not another Newcastle-born Haanah around the same time as the b.1893 Hannah, a NON-Newcastle-born Hannah Rose, and there were quite a few of them, including the one born West Bromwich in 1897, and some as close as County Durham, could easily have more to Newcastle area some time after her birth and married Ralph. (sorry about length of last sentence)
The only way to be sure, to be sure, is to buy a copy marriage cert for the 1913 marriage as already mentioned by Wozzle and Mum ( or avioding the cost of cert, by turning up their church marriage record, assuming they married in a church- but that might end up a more expensive option ! )
Michael Dixon