You should inform future partners, I personally know a couple with the same story and they both ended up with genital herpes. But, luckily, as long as you have no outbreaks present you probably won’t be passing it on to them.

I tell every partner I have! It's a hard thing to do but I think it's what's right. I got it the same way, through oral contact

I have HSV1 on my genitals as well. I have always told everyone I was about to be intimate with - I honestly wish whoever I got it from told me (but they might not have known - it’s also why I try to talk about STIs before getting intimate too now). You can still pass it when it’s not present, but it’s a lot less likely - I definitely only recommend having sex when it’s not present and you don’t feel any symptoms to be safe. And it’s just safest to use protection because you (even they) also might not know what they might have - they could always lie too.