‘Pompey’ is another mystery (or another origin of numerous urban myths). Other than the Naval connection, nothing is certain.
As far as the possible origins of the name are concerned, it’s important to realise that the medieval town was built alongside an inlet called the Pool. This was the mouth of a tributary into the Mersey and formed the city’s initial harbour. The Pool was eventually filled in during the early part of the 17th century and so the original contours aren’t apparent in the first detailed map of the city, that by Chadwick in 1725. However, its location can be deduced from the continuity of the surrounding street names and the area has also been reasonably excavated, since most of it underwent postwar development (the police station, the courts, the main road etc.).
On this modern map, the main part of the Pool roughly corresponds to Canning Place (arrowed), with the river coming in along the line of Paradise Street. Note that the original shoreline of the Mersey would have pretty much run along what’s now the A5036.
Regarding the name itself, the oldest surviving document using it is King John’s charter of 1207, in which the spelling is “Liverpul”, though the known existence of the town can be pushed back a little before that.
There are detailed reconstructed maps of the Pool and the medieval town - together with reproductions of the charter and the 1725 map, plus lots else - in the Archaeological Survey of Merseyside’s The Changing Face of Liverpool, 1207-1727 (Merseyside Archaeological Society, 1981).
Well after all that I guess that GorillaMan has the clearest answer, either from Welsh or old English.
By the way, the “liver bird” is not pronounced as in “liver”, the organ, but as “lye-ver”, to rhyme with Macgyver. But it’s not “Lye-ver-pool”, of course.
Wigan claim to be the “Latics”, but are competing with Oldham Athletic on that one. Rotherham are the “Millers”. Coventry are the “Sky Blues”. Leeds are either the “Whites” or just “United”. Reading used to be the “Biscuitmen”.
More:
Barnsley - Tykes
Blackpool - Tangerines
Bournemouth - Cherries
Bradford City - Bantams
Brentford - Bees
Bristol City - Robins
Chesterfield - Spireites
Colchester United - U’s
Hartlepool United - Pool
Huddersfield Town - Terriers
Hull City - Tigers
Luton Town - Hatters
Oldham Athletic - Latics
Peterborough United - Posh
Port Vale - Valiants
Sheffield Wednesday - Owls
Stockport County - County (may have been “Hatters” at one time too)
Swindon Town - Robins
Torquay United - Gulls
Tranmere Rovers - Rovers
Walsall - Saddlers
Wimbledon/MK Dons - Dons
Wrexham - Robins
Bury - Shakers
Darlington - Quakers
Kidderminster Harriers - Harriers
Leyton Orient - O’s
Lincoln City - Imps
Mansfield - Stags
Northampton - Cobblers
Notts County - Magpies
Rochdale - Dale
Rushden & Diamonds - Diamonds
Scunthorpe - Iron
Shrewsbury - Shrews
Wycombe - Chairboys
I notice that Scunthorpe are called Iron. The non-league team where I used to live , Braintree, also have that nickname. This is because they were originally a factory team formed by workers from an iron foundry.
Their local name (to non-supporters of course) was “Wigan Pathetic”, although they’re not that pathetic anymore 
Most people refer to them as the Latics around here.
Really? I thought they were the “seasiders”?
Both, I think.
Us Oldham fans refer to Wigan as the “Plastic Latics” due to the club’s relative lack of history.
Yes,so did I.
By the way, no points for for the nickname of my team, Swansea, but one point for what they call the supporters. Please keep it clean 
Agreed. But, more often than not, context is usual crucial in explaining why the clearest answer, even if properly equivocal in this case, remotely begins to be plausible. Particularly if that’s only (entirely usefully) been Googled.
Quite, and there is absolutely no need for anyone to be harsh towards Burnley. We’re very good at doing that ourselves, thankyouverymuch. 
I was a Leeds United fan when I was a kid (they were a top team at the time, and I’m not talking about 1992) and ISTR their nickname then was the Peacocks. Not the coolest sounding nickname, so perhaps they’ve quietly dropped it.
I thought Bolton were the Wanderers?
Newcastle officially is called The Magpies, but I have also seen them called Toon and the Geordies.
Yeah Toon is Geordie slang for Town (i.e. Newcastle the place)
Geordies are to Newcastle what Scousers are to Liverpool.
See, even as an American I know about Geordies. They’re the folk that speak some totally incomprehensible thing that sounds sort of like English.
I thought that was the Scots…
Geordie dialect isn’t a million miles from Scots. Once you get used to it you can tell the difference but it’s hard to tell them apart at first (or so I’ve heard).
The name of the Club is Bolton Wanderers, but the club nickname is the Trotters, in the same way that Man Utd are the Red Devils
The other nickname for Man Utd is of course The Scum.