How can I type the name of the person I'm calling on the dial pad and make the call?
In terms of an easier way, you have a number of options you can try. In addition to using the Contacts tab as pointed out by Nimesh Neema, you can also try:


Installing one of the many 3rd party apps, many of them free, that offer the functionality you're after (i.e. typing a contact's name via the dial pad)
Adding most of your commonly used numbers into your Favourites list
Using Siri to make calls, but not necessarily by saying, "Hey Siri, call...", but also by enabling the Type to Siri feature (more info below)
By swiping down from the middle of your screen to conduct a search and then doing one of the following:

-- start entering the name of your contact until you see them listed as your "Top Hit" and then tap on the phone icon to call them (or the message icon, etc)

-- enter the word "Call" followed by the first few letters of the name of your contact to get the option to call them 


Enable the 'Type to Siri' feature

On your iPhone do as follows:


Open Settings
Tap on General > Accessibility
Swipe up until you see the Siri label
Tap on Siri and enable the Type to Siri option at top of screen
Exit Settings


Now when you hold your Home button down (or in the case of an iPhone X or above, by holding the side power button) you’ll get a keyboard pop up from the bottom allowing you to type directly to Siri (see screenshot below):




Now type the word "Call" followed by your contact's name, or just type your contact's name to be presented with a contact card from which you can call, text, email, etc.