Surely we don't really need the dynamic SQL in there, we can just use:

declare @newName sysname

...

set @newName = @childname + '_' + @parentname + '_' + CAST(@soid as varchar(20)) + '_FK'

exec sp_rename @name, @newName

...

(And we don't really need the variable I added, it's just a bit neater).

We probably also want to have some kind of check for long table names, since sysname is "only" 128 characters (or less in earlier versions of SQL).