That would largely be up to your business to decide. You could certainly add custom profile fields to collect these details (if you wanted to snd something physical in the mail).

As @Scott Baldwin mentioned it will be down to your own company policy, but another solution to tackle this would be to have people opt-into it outside of InSided. Instead of storing their data within the platform which could be interpreted as having multiple uses (not just receiving gifts) you can have a dedicated form in which they fill their details for this specific purpose…
Alternatively if policy allows, you might be able to add a field that would allow them to determine what its for like a T-Shirt size field for example, which could appease their mind on this data collection. This is all greatly simplified if you already hold the physical address though, then you’re likely only dealing with bribe prevention clauses in B2B context.