Whether done on the same day as closing or a period of time later, you can transfer a property you own in your personal name to your business (e.g. LLC, corporation, etc.) or other entity you have controlling interest in (e.g. trust).
If you own the property without a mortgage, you can transfer ownership simply and inexpensively via a quitclaim deed.
This is a common way to work around the situation where your cash purchase Proof of Funds Letter is written in your personal name and thus your personal name is on the purchase contract.
A quitclaim deed (which carries no warranty/guarantee), as opposed to a warranty deed, is only an acceptable method of transferring ownership if the recipient/grantee agrees.
Because you’re transferring from yourself to your own entity — you personally are the grantor and your entity is the grantee — you’ll decide that your entity will find the quitclaim deed acceptable.
If transferring to an entity that you do not have a controlling interest in, a quitclaim deed will usually not suffice (although there are situations where title companies will recommend obtaining quitclaim deeds for other scenarios).
If your property is mortgaged, your mortgage note may have provisions disallowing such a method of transfer (i.e. requiring a warranty deed).
If you purchased a government-owned property, you likely signed a document restricting such a transfer of ownership for a period of time (e.g. 45 or 60 days).
Because of the “gotchas” that you may not be fully aware of, it’s always advisable to seek advice from a real estate attorney / title company for your specific situation.