By "Use labels as variable names," I assume you want to use nice labels on the X and Y axes on the fit plot. If so, use the LABEL statement inside the PROC REG step, like this
PROC REG DATA=WORK.FIGURE (RENAME = outcomes_adults_mental_distr = Frequent_Mental_Distress)
PLOTS(ONLY) = FITPLOT;
label Frequent_Mental_Distress= "Frequent Mental Distress"
Marijuana_Use = "Marijuana Use (Grams per Day)";
MODEL Frequent_Mental_Distress = Marijuana_Use / CLM CLI ALPHA=0.05;
ODS SELECT FitPlot;
quit;
It is possible to remove the MODEL : MODEL1 tag, but it is an advanced technique. Most people prefer to see a reasonable name for the model, such as follows:
options validvarname=any;
PROC REG... ;
/* specify a label before the MODEL keyword */
'Distress vs Marijuana'n:
MODEL Frequent_Mental_Distress = Marijuana_Use / CLM CLI ALPHA=0.05;
quit;