So you have different options to be honest.

What I do these days is the following.

1. I keep my raw values as they index by default
2. I create a new examine field with "cleaned" appended to the end (against which I do my searching)
3. I then take advantage of Examines ability to store multiple values against a single field:

Doing something a bit like this (my example is handling MNTP's)

internal static void HandleMultiNodeTreePicker(IndexingItemEventArgs e, IPublishedContent content, string property, IUmbracoContextFactory umbracoContextFactory, ILogger logService)
    {
        try
        {
            var processed = new List<object>();
            if (content.HasProperty(property) && content.HasValue(property))
            {
                IPublishedContent categoryNode;

                using (var umbracoContextReference = umbracoContextFactory.EnsureUmbracoContext())
                {
                    foreach (var entry in e.ValueSet.Values[property].Cast<string>())
                    {
                        foreach (var processedEntry in entry.Split(',').Select(s => GuidUdi.Parse(s)))
                        {
                            categoryNode = umbracoContextReference.UmbracoContext.Content.GetById(processedEntry.Guid);
                            if(categoryNode != null)
                                processed.Add(categoryNode.Name.Replace(" ", ""));
                        }
                    }
                }

                e.ValueSet.Values.Add($"{property}Cleaned", processed);
            }
        }
        catch (Exception ex)
        {
            logService.Error(typeof(GenericIndexHelper), ex, $"Error Handle {property} - {content.Id}");
        }
    }

In your case you'd code would be simpler as it would take a string, split it on ,'s to turn it into an array of string and index the array as individual items

Then that search I suggested would do the following:

if myFieldCleaned contains any of my search terms, return the result

At least that is my understanding