Вы можете сделать это с помощью цикла for и оператора if:
nametoRemove = input("Enter the name you want to remove:")
print(nametoRemove)
name = ["Ramesh","Rakesh","Suresh"]
for item in name:
if item.lower() == nametoRemove.lower():
name.remove(item)
print(name)
output:
Enter the name you want to remove:ramesh
ramesh
['Rakesh', 'Suresh']