"Late" usually refers to the name she was known by immediately prior to the wedding.
"Formerly" usually refers to the name she was known by previously (usually her maiden name).
I don't think, however, that there are hard and fast rules

The marriage certificate is Informant led - the registrar just writes what he is told.
And people (in the UK) have the right to call themselves anything they like - just as long as there is no intention to deceive or defraud.