That depends who you ask! Traveline had Hampshire and the cities of Southampton and Portsmouth as included in their SW Region. A potty decision (by the local authorities) as the vast majority of their transport connections are with South East counties (which included the Isle of Wight)
I would say places like Andover / Bournemouth / Salisbury / Portsmouth / Southampton / Weymouth are definitely South East. I have never heard anyone consider these to be in the South West. Traveline putting them in South West instead of South East was very unusual.Funnily I thought the opposite, in the Network South East years, I thought NSE had a odd presence here as Dorset is in the SW region then it changed into SWT, I thought that's better then I remembered about more SE region counties like Hampshire also being covered too.
SWT/SWR mostly centres around the SWML to/from Waterloo - see SWR's cyan blue logo, rather than geographically.
South Western Railway operate in the South West of London and in the South West of the South East England area. But they do not really operate in South West England other than the small bit around the Exeter area. I have always thought the TOC name meant either ths South West of London or the South West of the South East England area.
This is how i have always considered the regions:
South East - Bedfordshire, Berkshire, Buckinghamshire, Cambridgeshire, Dorset, Essex, Greater London, Hampshire, Hertfordshire, Isle Of Wight, Kent, Norfolk, Middlesex, Northamptonshire, Oxfordshire, Suffolk, Surrey, Sussex, Wiltshire.
South West - Avon, Devon, Cornwall, Isles Of Scilly, Somerset.
East Midlands - Derbyshire, Leicestershire, Lincolnshire, Nottinghamshire, Rutland.
West Midlands - Gloucestershire, Greater Birmingham, Herefordshire, Staffordshire, Shropshire, Warwickshire, Worcestershire.
North East - Durham, Greater Newcastle, Northumberland, Tyne, Tees, Wear, Yorkshire.
North West - Cheshire, Cumbria, Greater Liverpool, Greater Manchester, Lancashire.
But it is probably something up for debate. Different people will have different definitions of what falls in what regions. Especially more towards the border you get more debate.