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It's a surname - http://www.last-names.net/surname.asp?surname=Bromley :

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From Bromley, a small town in England, so called from brome or broom, and ley, a field or common.

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Also, from http://www.nottingham.ac.uk/english/ins/epncurrent/keytoepn.html :

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'Wood/clearing where broom grows'. OE brom, OE leah

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and 'Brambley wood/clearing'. OE braembel, OE leah

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I think bramble and broom are pretty much interchangeable in this context, but I could be wrong.