A registered mobile number with Gmail provides a few security benefits. Along with allowing you to recover your account in the case of lost password, you can also use it to login without a password.
But, if you want to change the registered mobile number on your Gmail account, you can use this procedure to do that.
Change Registered Mobile Number in Gmail
Step #1: Open Personal info & Privacy page for your Google Account. This will take you to the page where you can decide what you want Google to know about you. Scroll down a little and look for the Your personal info section.
Step #2: In the Your personal info section, click on the field named Phone. This will take you to the phone number privacy settings page.
Step #3: Click on the pen (edit) icon to actually edit your phone number. Depending on your activity level, Google might ask you to re-enter your password again.
Step #4: Click on Update number button. Now, enter the number you want to use for your Gmail account. Click on Verify button. Your phone will get an SMS with a secret code. Enter that in the next field and click OK.