Taylor Swift is known for writing songs about all her celebrity break-ups, and she is open about what when and who her songs are about. She is also known for having dated many people, hence the line '
Got a long list of ex-lovers'.
'
They'll tell you I'm insane' is either referring to the general public saying Taylor's insane because of all of her exes.
'
I've got a blank space baby, and I'll write your name'
Is saying she has a 'blank space' in her list of exes- she is single and ready for a relationship. She is also open that it probably won't work out.