the manx museum has town plans - dating from 1870 but there should be some late 1890's that will show street names - the 1894 directory (on line in Manx notebook lists douglas streets and you should be able to find any Ramsey st)
Judging from comments at time most single mothers had their child at the Braddan poor house - there was a poor house in Ramsey (just down from St Pauls in Chrush st , now demolished) but I don't know if it provided the same service