A few years ago I traveled to America under a different name to my birth name and had my fingerprints and retina scan taken I’ve since changed my name back to my birth name will this cause me a problem in returning to America
If you are open about the name change and that you have been in the USA, and under which name, the fact you changed your name is not a problem.
If you broke rules and would not be allowed under your previous name you have a very big chance you will not be allowed this time.
If you try to hide your previous visit and are found out on that a ban is likely and that will affect more than 'just' travel to the USA as many countries do not trust people who got a ban to enter a country.
With the USA you can or have to apply for a visa and if you are honest in the application you run little risk when travelling, but the USA does not guarantee you are allowed in with a visa.
While I have answered for the USA, in most countries it will work the same, only it is not always possible to apply for a visa when you come from a country of which the citizens do not usually need a visa. But in most countries it is that if you have a visa you are good to get in unless you did not disclose the name change and previous visit.