In a land far, far away, names have an expense based on the cost of each letter.

Create a function that calculates how much a name will cost based on a dictionary provided as a parameter, where the keys are lowercase letters and the values are their respective costs. The function should ignore any characters not present in the dictionary.

Example:

letter_costs = {'a': 1, 'b': 2, 'c': 3}
name = "Abc"
cost = calculate_name_cost(letter_costs, name) 
# Returns 6 (1 for 'a', 2 for 'b', and 3 for 'c')