Fetching data from a database
You can try the .Any function on IQueryable. It is made for checking if there are any records.

Remember that .Any() has an overload that takes an expression, making the solution 

internal static bool WellExists(string name, DatabaseContext context)
{
    return context.Wells.Any(x =&gt; x.Name == name);
}


I'm going to add a comment about your code as well.
In the second example you have return !(well == null). This obfuscates the meaning of the code a bit, and would be clearer if you write return well != null;