The most common suggests comparison to Blackpool (the inlet with water coloured black after running through a peat bog), Dublin (Gaelic for Black Pool for similar reasons), Hartlepool (probably the inlet named after the Hart or stag), and that the name either comes from a pool which is the colour of liver (dark red from the bogwater), or ‘muddy pool’ from a linguistic derivation.
In the same family of reasons we have Llifpwl from the Welsh (‘inlet that floods’), which has some reasoning behind it given the tidal range of the Mersey and the fact pre-domesday trade was probably primarily Welsh and Irish, plus of course the fact it is often the outsider or visitor who needs to name a place more than the peasant who lives there and never goes anywhere else. The Welsh ‘place of the pool’ is another possibility.