This error means that the expression has optional value (the value can be nil) that is not yet unwrapped, strName.first returns an optional value of Character?, but your function demands a returning type of String which is not an optional type.
So, in order to fix this, you need to unwrap the optional value strName.first, it seems like you are not familiar with optionals, here's the code for your case (choose one from two options):
func getFirstCharInName(strName: String) -> String {
    // option 1: force unwrap - can cause fatal error
    return String(strName.first!)
    // option 2: optional binding
    if let firstCharInName = strName.first {
        return String(firstCharInName)
    } else {
        // if the optional value is nil, return an empty string
        return ""
    }
}
PS. I don't really understand the function trim() in your question, but if you mean to strip away the blank spaces like "  ", you can do:
firstCharInName.trimmingCharacters(in: .whitespaces)