General :: Delete Files With Complex Filenames With A Script?

I am trying to write a bash script to delete a file where I know the first part of the name, but it has spaces in it. The second part of the file name is a random set of characters. I was hoping to use a wildcard for this, but I keep getting a error massage saying file or directory does not exist. This is a simplified form of my script:

Code:
MYFILE=This is my file
rm "$MYFILE*"
The file may be something like "This is my file.123abc456.suffix"