"Entry$()" holds all keys pressed since the program was ran. When you use "clear entry buffer" it removes all text that has been saved. You can get one letter by clearing the buffer before the loop then making a string = "entry$()" and clearing the buffer again.
If you want things to happen while the input is working just add it inside the do/loop.
sync rate 0
sync on
make object cube 1,1
Name$=""
clear entry buffer
do
if Name$="" then n$="None" else n$=Name$
text 10,10,"What is your name? "+n$
a$=entry$():clear entry buffer
if asc(a$)=8 then Name$=left$(Name$,len(Name$)-1):a$=""
if asc(a$)=13 then exit
Name$=Name$+a$
rotate object 1,wrapvalue(t),0,0
inc t
sync
loop