If you have committed any offences which require a Notice of Intended Prosecution (NIP) and a Request for Driver's Details (S172 Notice) they will go to the person named as the Registered Keeper on the records held by the DVLA. Eventually somebody will name you and you will get your own NIP and S172 notice.

So I got a car from the dealership second hand about a month ago but found out the logbook hadn’t been updated by them to change the owner to me What does this mean in terms of fines and speeding tickets if any, do they still apply to me and if so how do I find out

There's a massive paper jam at DVLA as staff have not been able to work normally because of Covid lockdown and difficulty of getting the place Covid safe for the future.

Were you able to taxi it at time of purchase? Last few times I've bought a car that's been done on line at the sales rep's desk when taking delivery.