Alice,

I totally understand your confusion, and indeed the name of 3dDeconvolve is very misleading. Since the basic framework was laid out and written in the ancient time, it's hard to make changes about the name now.

More accurately 3dDeconvolve is essentially a regression program with ordinary least squares approach. If you model the HRF with TENT basis functions (or multiple lags with -stim_files), that would be a real deconvolution since you don't make any assumption about the HRF shape, but you can also interpret it as a regression model through multiple basis functions. With other basis functions such as GAM or BLOCK, it's essentially a regression model with no deconvolution involved at all.

Gang