I am about to submit my first app to the Apple app store.
Let's say that it is called "GreatClock". There is already an app on the market called "great clock". There is some variable spelling, different capitals and a space.
I have registered my name with Apple. Will this create a legal conflict?
It is possible you are infringing another's trademark. More important than registering the name with Apple is clearing it and registering it with the government. It may not matter that there are slight differences in the two names. If it is likely to cause confusion, registering it with Apple and offering it for sale may be infringing acts.
During any due diligence for a contract involving your product, this issue should arise, and it will be your duty to comply with your buyer's requirements.
You can search registered trademarks here:
Choose a different name. You have a moral as well a legal reasons to do so.