I was having the same issue (I believe there is no ubuntu password for an AWS EC2 Instance and R studio requires one).
You can add a new user by typing the following: sudo adduser YOURUSERNAME
and follow the terminal instructions (press enter to skip the info you do not want to give). Head over to the IP xxx.xxx.xxx.xxx:8787 and you should be able to log in now.
How to install R studio 3.4.4, upgrade to 3.6.0 and add a username (Ubuntu 18):
sudo apt update
sudo apt-get install -y r-base r-base-dev
sudo apt install gdebi-core
wget https://download2.rstudio.org/server/bionic/amd64/rstudio-server-1.2.1335-amd64.deb
sudo gdebi rstudio-server-1.2.1335-amd64.deb
sudo chmod 777 -R /usr/local/lib/R/site-library
sudo adduser YOURUSERNAME
#########
# Upgrade R
echo "deb https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/" | sudo tee -a /etc/apt/sources.list
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys E298A3A825C0D65DFD57CBB651716619E084DAB9
sudo apt-get update
sudo apt-get upgrade -y
sudo apt-get install -y r-base r-recommended r-base-dev
# Rstudio dependency issues (when installing devtools) - I installed from an AWS EC2 account so I need to change my root password.
sudo passwd root
su root
apt-get -y build-dep libcurl4-gnutls-dev