First questions: Does dad pay child support or are you raising your son on your own with social input from dad ? Does he help make medical and social decisions for his son, or do you make all the decisions, and he comes over for play dates? Who is paying for pre-school?
Your name used to tell who was your next of kin. So when she got married, a woman changed her last name to match her husaband's, because he was now her closest legal relationship. Your son is your next of kin. The problem is that he is also his father's "next of kin", even though you two are unrelated. I have friends who got married as equals and hyphenated their names. Hers first (alphabetically), then his. They've been married for 21 years now, and even though their kids also have the same double name, no one uses it. They all use the dad's last name. I think it just got eaiser conversationally. But I suspect legally, their names continue to be double last names.
That said, your son's preschool records won't be going anywhere. (Like on to kindergarten and elementary school) I would think that you could enroll him with his full, legal name, and then let them call him by your last name so he doesn't have to use both. Who will be picking him up from pre-school ? Will his dad be involved or even know ? Frankly, when my kids were that age, they used their FIRST names on the papers they colored, and maybe a last initial. And since he has two last names, P would be the first initial of his multiple supply. No problem.
You can say you shortened it to make it easier for the other kids, but it really won't matter in the long run. Hispanic kids ALL have 2 last names. And I don't see a problem with having two last names. As your son goes on into elementary school, you will find scads of kids with last names that don't match either parent they are living with. Schools are used to dealing with this. At the same time, when I got divorced from my older kids' dad, I kept his last name, to make life easier for everyone. I wanted my name to match my next of kin -- my children. Later, I began to consider going back to my maiden name because it said more about who "I" was, and his last name was beginning to feel foreign to me. Before I made any decisions on that, I remarried, so then my name matched my current husband's name, and we have two more kids. But even with different last names, there is no question about who is sister to whom (we have 4 girls, 2 & 2). They KNOW who their sisters are, and the fact that my older girls have a different last name than the others in the family doesn't make any difference to anyone (except maybe their dad who extricated himself from their lives when he remarried, and is now working his way back in -- now that they are adults) Children are very accepting of differences, and will simply accept your son as having two last names. No problem.
I have been re-married for 20 years now, and I still answer to Mrs. "ex-hub's" last name on occassion. It doesn't bother me. I know the person knows one of my daughters and they are addressing me as her mom. So I answer as addressed. If someone asks me if I am Mrs. S, I say, "Yes, but no." and grin. I am the person they are looking for (my child's mom), but not by that name. It's not a big deal.
If you think it will anger his dad, then I wouldn't make any changes at all. If it makes you feel better, you can add a hyphen to the double last name, even though you wouldn't use that on a tax return because the double last name is his legal name on the Social Security System records.
When/if you son gets married, then HE will want to decide what his name is going to be, cuz he is most likely not going to want to have 3 last names ! But two is not that uncommon, and I think it's a neat way of affirming his geneology. We should all be hispanic and do that as a matter of culture.