You might want to distinguish between displays of raw survival data like Kaplan-Meier curves and survival functions predicted from a semiparametric or parametric model. For example, "proportion" might most directly represent raw data while "probability" might represent model predictions. Thanks to @periwinkle for the helpful link about that distinction. Even that distinction gets a bit fuzzy, however, as raw Kaplan-Meier curves are generally presented with modeled confidence limits.
Whichever you choose, make sure that the numeric axis labels agree with the text label. If you use "Percent survival" then the y-axis range should be 0 to 100. If it's "Survival probability" then the range should be 0 to 1.