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If it's her birth surname, this could be significant. If the two names are a 'good match', or have significance for her fictional parents, that would take your story one way. If they are a 'bad match', eg Madison Grayson, that would also impact on your story line. But if she's married and chose to use her partner's ln, then you might consider if she's (a) very much in love (b) happy to escape from, eg, Grayson and stay with Madison or (c) trying to put her past behind her for some reason.

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Without some knowledge of all that, it's hard to make a useful suggestion.