Lloyds Bank has been relaunched on to the high street as a standalone brand for the first time in 18 years after its split from TSB.
The "revitalisation" of Lloyds means the bank, which has a 250-year history and 1,300 branches across England and Wales, has changed its branding to reflect the dropping of TSB from its name as well as changing its website from lloydstsb.com to lloydsbank.com.
The new TSB bank appeared on the high street earlier this month after Lloyds offloaded 631 branches and eight million accounts to meet European competition rules.
TSB customers were initially expecting to be transferred to the Co-operative Bank but the deal collapsed earlier this year and Lloyds now plans to float the TSB business in 2014.
Lloyds customers using internet banking will be able to continue to use the same passwords and their existing banking terms and conditions will also remain the same.
The bank has also tweaked its mortgage range, including extending a £500 cashback offer for first-time buyers with a 10% deposit to more mortgage products for first-time buyers with deposits between 10-25%.
Around 4,000 customers who did not want to move to TSB had their request to stay with Lloyds granted, while around 600 Lloyds customers made the unprompted decision to move to TSB.
Lloyds' name was merged with that of TSB in 1995. Customers of both Lloyds Bank and TSB can still use both branded banks for now to give them time to adapt to the changes.
This means that a TSB customer still has access to everyday banking services through a Lloyds Bank branch and vice versa.
Owen Woodley, managing director, Lloyds Bank Retail, said the relaunch marks "another milestone in Lloyds Bank's history".
He said: "The revitalisation of the brand is an exciting time for the bank but also for our customers."
A publicity blitz surrounding the relaunch of TSB earlier this month was overshadowed by a computer hitch which meant that customers were unable to log on to internet banking at TSB and parent bank Lloyds.
Lloyds Bank began life as Taylors & Lloyds in Birmingham in 1765. It was founded by Sampson Lloyd II, John Taylor and their two sons. Each invested £2,000.
Last week, Chancellor George Osborne hailed the taxpayer's £61 million profit on the sale of shares in Lloyds Banking Group as more evidence that the economy was " turning a corner".
Mr Osborne claimed the £3.2 billion sale of a 6% slice of the bank to institutional investors represented a half-billion pound boost to the public accounts, because of the way it is valued on the Government's books.