There seems to be two different reasons for naming a station '### Road'. The first is that it is simply situated on that road: Wandsworth Road station is where the line crosses the Wandsworth Road (the next station is Clapham High Street, where the line crosses that street). The second is a station on the road to the town that was not served by a railway... and is usually a fair distance away, sometimes several miles. The suffix Parkway is the modern equivalent of the second definition of the Road suffix.
Re the bolded -- indeed so: quite a common convention earlier-on in the railway era -- in my perception, in England and Wales anyway; less so in Scotland. Examples are mentioned in this thread. Llanbister Road (I didn't manage to "quote relevant post, to respond to") -- in wild and hilly Wales, some 5 -- 6 miles from the quite sizeable and prominent village of Llanbister.
Beaulieu Road isn't actually near any road called Beaulieu Road (please correct me if I'm wrong, I've tried to look for it a few times on a map), and is miles off the village of Beaulieu. In fair honesty I don't know what you'd call it? Hatchet Lane?
Beaulieu Road -- an example of the bolded above: 3 -- 4 miles from the prominent New Forest settlement of Beaulieu -- actual local names of roadways, not relevant here. (The next station up the line from this one, was long named Lyndhurst Road, being 2 -- 3 miles from the prominent and well-known village of Lyndhurst; in more recent times renamed, with greater geographical precision, Ashurst New Forest.)
A paradox re this " ****** Road " station-naming custom which has always amused me, and which I have mentioned elsewhere on these Forums: concerning the village of Wansford, west of Peterborough. Wansford station (now on the preserved Nene Valley Railway) was the junction point of the LNWR's Peterborough -- Northampton, and Peterborough -- Rugby, routes; it was also reached, at a relatively late date, by a branch of the Great Northern Railway running south from Stamford. At the point of intersection of this Stamford -- Wansford branch, and the Peterborough -- Leicester main road, now the A47: an intermediate station was instituted, called Wansford Road. In fact the GNR Wansford Road station, one mile east of Wansford village, was closer to the village, than the LNWR Wansford "plain and simple" station, which is situated one mile and three quarters south-east of the village.