You are not the first person to do this. When Comte Sanche de Gramont became a US citizen he was allowed to adopt a new name as part of his naturalization. He chose Ted Morgan, because he wanted an easy American sounding name. He also had to renounce his title as a count.
In reverse, I had a friend with the first name Hon Wah, and he was always promoted to Honorable as his title. A lot of American blacks gave their children names like Duke or Lord, because white people never called them by their proper title (Mr., Mrs. or Miss back then). They just used their first names.
Lily is a great choice. It’s a pretty name. It’s easy to remember. It even sounds a bit like your old name. Good luck. Here’s hoping it fits you well.