My conclusion from what is detailed below is that Bute Terrace was built after 1904 and quickly became known as Mona Street (specifically, it was the houses on the south side of Mona Street).
In the Electoral Registers of 1909, Colne Valley, Township of Slaithwaite there are two people listed who include Bute Terrace in their address:
John William Carter, 5, Bute Terrace, Mona Street
Thomas Henry Shaw, 15 Bute Terrace, Mona Street
In the 1911 census a Thomas Henry Shaw is at 15 Mona Street. [The only candidate that I see for JWC is at nearby Royd Street.]
Going along the odd-numbered 1911 entries for Mona Street there is:
David Mosley at no.9 has written in 9 Bute Street on the main page but the enumerator has entered 9 Mona Street.
The same thing has happened at no. 41: the resident has used Bute Street, the enumerator, Mona Street.
At no.45 the resident has used Bute Terrace, Hill Top [no number]; the enumerator has used 45 Mona Street.
At no. 47, resident has Bute Terrace, Hill Top; enumerator has Mona Street.
Here is an overlay map view of Mona Street with the overlay set to 0% to show the modern map with house numbers. The odd numbers in Mona Street are on the south side. Increase the overlay to 100% to reveal the situation on the 6 inch map from 1904 (published 1906). Mona Street is not built at that date. It is however shown on the later map that I linked to in reply #6
https://maps.nls.uk/geo/explore/#zoom=17.7&lat=53.62569&lon=-1.88268&layers=168&b=osm&o=0Going from this evidence, and from the absence of newspaper references to Bute Terrace (apart from the Jagger advertisements) or indeed to Bute Street, I conclude that the name Bute Terrace was quickly replaced by Mona Street.
