On both DL/AA, I had no trouble getting precheck when it was just a variation of my first name (i.e. Alex vs Alexa/ Tom vs Thomas/ Jeff vs Jeffrey/ Tiff vs Tiffany and so on).

For a while, my passport name didn't match my drivers license name, and I used to use different name (but all with same First Initial & Last name) for domestic flights vs international flights, and no once, was I denied access to TSA PreCheck.