Need help in optimizing the process

I need help in optimizing my process. Here is what am I doing:
I have two tables table A and table B. table A has list of names and table B has name and ID. Right now I am loading name into cursor from table A and for each name from the cursor I try to match with name in table B to get the ID. This process takes very long to complete. I need help to replace PL/SQL with SQL if possible. I am using oracle utl_match to match the best possible record in table B. table B sometimes returns multiple matching records. I take the top nearest match name and ID for my use (there is not always one to one match)
Any idea or help will be appreciated. Thanks

always provide create table and sample data instert statements when asking a question. also, provide your database version.
because you're using utl_match, you can't really use an index, there must be a cartesian join on the two tables so it may always be slow.
however, here's a sample SQL that you may be able to make use of:
with n as (select 'KATHERINE' person_name from dual
             union all
             select 'STEVE' from dual
             union all
             select 'BRUCE' from dual)
    ,nid as (select 'CATHERINE' person_name, 1 NID FROM DUAL
             union all
             select 'STEFAN', 2 from dual
             UNION ALL
             select 'STEVEN', 2 from dual
             union all
             select 'CATHY',3 from dual)
select n_name, nid
  from (
        select n.person_name N_NAME
              ,nid.person_name
              ,nid.nid
              ,ROW_NUMBER() OVER (partition by n.person_name ORDER BY utl_match.jaro_winkler_similarity(n.person_name,nid.person_name) DESC) jws_ORDER
          from n
          join nid on (utl_match.jaro_winkler_similarity(n.person_name,nid.person_name) > 70)
  where jws_order = 1;    

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