Does anyone know what this yellow putty is called, and where I can find it?

silastic, I think. No idea.

Generically it's known as "staking glue", but that isn't a specific type of glue, more a description of what it's being used for.

Often it's an industrial hotmelt adhesive. Being that yellow colour, it could easily be 3M 3748 or 3748-V0. Hotmelt staking glue is quick and easy to apply in a factory setting and it's pretty strong.

Or it could be a silicone based glue, they are also common, but often they are a white colour. Silicone glues can be more flexible and maybe a bit cheaper, but they are messier to apply and have a much longer drying time.

Edit: 3M 3748 is available from digikey for around 5 dollars a stick, but you will also need a "polygun" applicator, which are a few hundred dollars.

Generic factory glue, something like hot glue should work.

I use GE Silicone 2 for this.