The street name is a girl's name (6)
I believe the answer is:
stella
'a girl's name' is the definition.
'the street name' is the wordplay.
'the street' becomes 'st'.
'name' becomes 'ella' ().
'st'+'ella'='STELLA'
'is' is the link.
(Other definitions for stella that I've seen before include "Paul McCartney's daughter" , "____ McCartney, fashion designer" , "lady?" , "- Gibbons (Cold Comfort Farm)" , "woman" .)