The Inman Estate covered a fair amount of territory; Ralph Inman died in 1788 and the land was sold to Leonard Jarvis, an unsuccessful real estate speculator (There is a Jarvis Street in Cambridge - it is about 50 feet long but not in mid-Cambridge.) The estate was split up and one of the owners was Jonathan Austin (Austin Street is now called Bishop Allen Drive). Subsequent owners were Benjamin Bigelow and then Nathaniel Cabot Lee - who got street names. In 1804 after Lee died the land was purchased by Royal Makepeace (no street name). He divided up the property and had some streets built including West Street - I found no information in this book about why West was chosen. I did find a record that the street was named in 1806. Starting in 1830 some houses were built in this section. I found an 1854 map that has a house where mine is, I don't know if it is the same house, but it probably is. I vaguely recall once seeing an ~1860 map that had no house there and an ~1870 map that had one - but my dates might be wrong. It is clear that my house was built between 1830 and 1870 and it has had 3 major renovations (one that we did in 2001) each made it bigger. In a Harvard archive I found the existence of a record of a deed on file for an 1838 transaction, and a record of a house tax paid in 1839.
I will be doing some more research to figure this out. (I see there are some West Family archives at the Historical commission but its first member came to the US in the early 1900's so that's not it).
See the Google map of the area
The street with no name that runs into Inman St and has Austin Park branching off it is Bishop Allen Drive (formerly Austin St).
(1) The book is the Mid Cambridge edition of the Survey of Architectural History in Cambridge - published by the Cambridge Historical Commission in 1967.