Name adopted by one 'Lisa,' maybe (5)
I believe the answer is:
alias
'name adopted' is the definition.
'by one lisa maybe' is the wordplay.
'by' means one lot of letters go next to another.
'one' becomes 'a' (a thing is one thing).
'maybe' is an anagram indicator.
'lisa' is an anagram of 'lias'.
'a' put next to 'lias' is 'ALIAS'.
(Other definitions for alias that I've seen before include "aka" , "False or assumed name" , "Also known as" , "one's assumed" , "Otherwise called" .)