For SQL2017 and later, you could use the example of renaming a key
(which might be a bit cumbersome and might not work properly in case of duplicate keys)
declare @j1 nvarchar(max);
select @j1 = N'{"201902":121, "201902":145, "201903":134, "201904":513}';
select @j1 as before;
select @j1 = JSON_MODIFY(JSON_MODIFY(@j1, concat('$."', left(a.[key], 4), '-', right(a.[key], 2), '-01"'), CAST(a.value AS int)), concat('$."', a.[key], '"'), null)
from openjson(@j1) as a;
select @j1 as after, isjson(@j1);
Or handle json as a string with a simple REPLACE()
declare @j2 nvarchar(max);
select @j2 = N'{"201902":121, "201902":145, "201903":134, "201904":513}';
select @j2 as before;
select @j2 = replace(@j2, a.[key], concat(left(a.[key], 4), '-', right(a.[key], 2), '-', '01'))
--if keys appear as values...
--replace(@j2, concat('"', a.[key], '"'), concat('"', stuff(a.[key],5, 0, '-'), '-01"'))
from openjson(@j2) as a;
select @j2 as after, isjson(@j2);