yes. 16GB is pretty much the standard these days because a lot of newer AAA titles are starting to require a full 8GB just for the game at minimum requirements.
New system is a good idea, and can easily find an upgrade that works for a budget with Ryzen.
I'll just throw you a platform upgrade real quick because you already have everything else that can be reused.
This is for a Ryzen 2000 Series upgrade.
PCPartPicker Part List
CPU: AMD Ryzen 5 2600 3.4 GHz 6-Core Processor ($119.99 @ Newegg)
Motherboard: MSI B450M PRO-M2 MAX Micro ATX AM4 Motherboard ($74.99 @ B&H)
Memory: G.Skill Aegis 16 GB (2 x 8 GB) DDR4-3200 Memory ($54.99 @ Newegg)
Total: $249.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-12-07 18:34 EST-0500
And this is for a Ryzen 3000 series upgrade.
PCPartPicker Part List
CPU: AMD Ryzen 5 3600 3.6 GHz 6-Core Processor ($189.99 @ Amazon)
Motherboard: MSI B450M PRO-M2 MAX Micro ATX AM4 Motherboard ($74.99 @ B&H)
Memory: G.Skill Ripjaws V 16 GB (2 x 8 GB) DDR4-3600 Memory ($59.99 @ Newegg)
Total: $324.97
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2019-12-07 18:36 EST-0500
This build is also simply reference and theoretical since price and availability of components varies from country to country and I live in the US so this selection of components is based on the assumption that you do too.
Also, this build is simply choosing the more budget friendly options for motherboard, RAM, and CPU.
Could obviously go higher end with components but defeats the purpose of saving money.
Also, this is all assuming that your current PSU is good enough for the newer CPU's.
Otherwise you may want to look at upgrading the PSU.
And one last thing is that while you can overclock on this B450 board that I've chosen (btw, I specifically chose the MAX variant because it's newest and supports 3000 series out of the box) you won't be overclocking all that much.