It is, in my view, almost certain that Scotland would take on the current UK State Pension and turn it into a new Scottish Universal Pension. There is no fund and it is paid out of tax so there is no reason why we would not do so. Typically there is about £15-20 billion in the National Insurance Fund at any one time, so we could claim £2 billion or so of that as transition funding which would cover maybe two months. We will be collecting our own tax and having our own currency after that so paying it isn't going to be a problem (and taxes don't fund spending, but the other way around).
It is also existing SNP policy to raise that pension to about S£300 / week which is the current EU average (£16,000 pa). The current UK state pension is the lowest in Europe.
So in practicalities if you are resident in Scotland at midnight on Independence Day then your state pension / national insurance record will transfer. If you are a current pensioner ScotGov will take on paying your Scottish Universal Pension. If you are still working then your record will go towards a SUP and not a UK pension. If you are Scottish but in Spain for example getting a UK state pension then that will continue to be a rUK responsibility. You would not get the new SUP unless you return to Scotland before Indy Day. Anyone moving from rUK to Scotland after Indy Day will continue to have a rUK state pension entitlement. They will not get any SUP unless they establish an entitlement by working in Scotland. There may be some negotiation between Scotland and rUK that might allow a transfer of pension entitlements, but at estimated payment rates then you would need two rUK years to earn 1 SUP year. International transfers of state pension rights are rare so this may not happen, in which case you might get say 25 years in the rUK scheme and 15 years in the ScotGov scheme.
For company schemes: The ScotGov, Scottish Health Service, Local Government, Police etc schemes are all already Scottish and will be paid in S£ at whatever rates have been agreed with the unions. These cover around 500,000 people. Company schemes will be paid as contracted, but where the scheme is rUK (e.g. British Airways Pension Scheme) then it will be paid in Sterling and you will have an exchange rate risk. If it is a Scottish company scheme such as Scottish Widows, RBS, etc then it will be paid in S£ at the agreed rates.
For private pensions, SIPPS, etc then it depends on whether the provider is rUK or Scottish. So e.g. if you use Aviva then they are an rUK company and will most likely continue the scheme in Sterling and pay in Sterling. If it is e.g. a Standard Life plan then you should have the option of switching it to S£ with payments then in S£.
If you e.g. retire to Spain after Indy Day then ScotGov would pay your SUP and any increases to you in Spain in S£.
If you move to rUK after Indy Day then if you are already a pensioner ScotGov will pay your SUP in S£. If you are still working then your number of years entitlement to the SUP will freeze at the current level (there may be a scheme for voluntary contributions as there is now with the UK state pension) and you would start to accumulate years in the rUK state pension scheme.