My batch code skips past if statements

NOTE: This is not a duplicate because the other questions I found are not the same goal as mine and is a different if statement.

I wanted to make a batch file that can remember your name, even after being closed. It saves the name in a text file and then reads from it. My question is it skips past my first if statement. Why does it do this? When I type y it goes to :no. I think this is because right after the if statement is the :no part, but what am I doing wrong? If you don't understand this, just copy this code and paste in notepad and then save as ANYTHING.bat and run it, and you'll see what I mean.

Anyway, here is the code:

@echo off
title The logger
echo NAME> log1.txt
set /p name=<log1.txt

:start
cls
echo Your name is %name%, right? (Y/N)
set /p input=
if %input%=="Y" goto yes
if %input%=="y" goto yes
if %input%=="N" goto no
if %input%=="n" goto no

:no
echo Oh... then what is it?
set /p name=
echo OK! Thanks, %name%
echo %name%>log1.txt
pause
goto start

:yes
echo hahahaha i knew it
echo Would you like to change it? (Y/N)
set /p input=

if %input%=="Y" goto namechange
if %input%=="y" goto namechange
if %input%=="N" (
    echo Ok.
    pause
    goto start
)
if %input%=="n" (
    echo Ok.
    pause
    goto start
)
goto start

:namechange
echo What should it be?
set /p name=
echo %name%>log1.txt
echo Thanks, %name%
pause
goto start