Currently employed and planning to immediate resign before background check in new company

Hello po. I need help. I’m currently employed at a company where I’ve been working for around 2 months palang, but I’m already planning to quit because the location is really difficult for me.

Last week, I accepted a job offer from another company that’s much closer to my location and I’m planning to move there. The thing is, I didn’t declare to the new company that I’m still employed. I was planning to resign immediately once I got the offer. I was afraid they wouldn’t hire me if they found out I was still employed, especially since I’ve only been with my current company for 2 months.

Now, I’m in the background check process with the new company. Should I resign immediately? Will my new employer find out that I’ve been working at this company for just 2 months? Will it cause problems for my new employment since I didn’t declare it and am only planning to resign now?