Compare two person name (Are the names similar?)

Working on a personal project I need a mechanism to compare two names and find out if they are similar. The first think that I done was to try to define a regular expression that could help me.
I end up studying different algorithms that can measure the distance between two sequences.  In this post I will talk about what algorithms I found and what I finally used.
First algorithm that I found was the based on Hammed distance. This algorithm measure the minimum number of substitutions that need to be done to change a string to another string. This is a great algorithm that works very well when we have string with the same length.
Another interesting algorithm was based on Euclidean distance and is used to measure the distance between two points. It is based on Pythagorean formula. It is a pretty complicated algorithm and in my case was too complicated. I need a simple solution, that doesn't consume a lot of resources. I don’t need exact match each time.
The 3th algorithm that I discover was Jaccard similarity coefficient. Using this solution you can obtain the similarity and diversity value of two sets – in our case two strings.
In the end I found what I need. The Levenshtein distance compare two sequences and measure the difference between them. It will give us how many changes we need to make to the first sequence to obtain the second one.
It is pretty similar to Hammed algorithm, but in my case this solution is good and resolves my problem. The algorithm returns a positive number. In my case when the returned value is 2 or lower I consider that the two names are similar.
Of course there are also a lot of solutions, different components that resolve this problem. In my case this was the perfect solution. The implementation in C# can be found at the end of the post.
You will observe that the algorithm is recursive. We can rewrite it in different ways of course.

Recursive version:

int LevenshteinDistance(string s, string t)
        {
            int n = s.Length;
            int m = t.Length;

            if (n == 0)
            {
                return m;
            }
            if (m == 0)
            {
                return n;
            }

            int cost = s[n - 1] == t[m - 1] 
                        ? 0 
                        : 1;
            
            return
                Math.Min(
                    Math.Min(LevenshteinDistance(s.Substring(0, n - 1), t) + 1,
                                LevenshteinDistance(s, t.Substring(0, m - 1)) + 1),
                    LevenshteinDistance(s.Substring(0, n - 1), t.Substring(0, m - 1)) + cost);
        }

Non recursive version:

int LevenshteinDistance(string s, string t)
        {
            int n = s.Length;
            int m = t.Length;
            int[,] d = new int[n + 1, m + 1];

            if (n == 0)
            {
                return m;
            }

            if (m == 0)
            {
                return n;
            }

            for (int i = 0; i <= n; d[i, 0] = i++){ }
            for (int j = 0; j <= m; d[0, j] = j++){ }

            for (int i = 1; i <= n; i++)
            {
                for (int j = 1; j <= m; j++)
                {
                    int cost = (t[j - 1] == s[i - 1]) 
                                    ? 0 
                                    : 1;
                    d[i, j] = Math.Min(
                                    Math.Min(
                                        d[i - 1, j] + 1, 
                                        d[i, j - 1] + 1),
                                    d[i - 1, j - 1] + cost);
                }
            }
            return d[n, m];
        }