Like in Lambda Expression and LINQ

customers.Where(c => c.Name.Contains("john"));

If you are targeting LINQ to SQL, use SqlMethods.Like:

customers.Where(c => SqlMethods.Like(c.Name, "%john%")); 

Explanation:

The compiler will generate an expression tree from the statement above. Since LIKE is a SQL specific construct and not common to all LINQ Query providers, the SqlMethods class and its members are used as a "hint" for the expression compiler (compiles expression trees to SQL) to emit a LIKE statement.

The first thought that comes to mind is Regex.IsMatch.

This would come closest to providing the kind of functionality you get from LIKE; for instance with it you could do this:

var matches = people.Where(p => Regex.IsMatch(p.Name, "A.*[mn]"));

foreach (Person match in matches)
{
    Console.WriteLine(match.Name);
}

And get output like this:

Adam
Aaron
Aidan

Going with string.Contains as others have suggested is almost certainly preferable if your intention is simply to look for a specific substring within Name.