When assigning Intellectual Property (IP) to the company, it's important to determine who is the current owner of that IP. The creator of that IP will almost always own the IP, but you need to consider whether the creator was working independently or as an employee of a business. 

For example, think about hiring a design agency to create a logo. In that case, the creator of the IP is the agency, even if it was only one employee who did all the work on the logo.
In another case, you could have hired an independent designer to make the logo. If this is a self-employed individual that person is the creator of the IP.
You can always check with the creator of the IP to determine if they were working as an individual or as a representative of a company when they created the IP.

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In an IP assignment agreement, you can specify the specific items of intellectual property you want to assign from a creator to the company. Or you can make the agreement broader by stating that "all work" done by the creator for the company will be assigned. The broader rights are generally more beneficial to the company, as it ensures all IP is covered. For the creator, they may prefer a narrow and very specific items of IP (like a logo or website design).
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Moral rights include the ability to take credit for a piece of work and determine how it is used after ownership has been transferred to someone else. It is common for moral rights to be "waived" or transferred to the company along with the IP. But in some cases, like works of art, the creator continues to hold the right to attribution, the right to ensure the artwork isn't modified, and the right to include the artwork in a portfolio.

The assignment of IP has distinct value, which must be included as a separate payment in the IP assignment agreement. While you may have already paid for the IP, that payment is separate from the assignment agreement. Often an IP assignment agreement will include only a nominal payment (like $5.00) as a formality. In legal terminology, this is referred to as the "consideration" for entering into the assignment agreement. 

When assigning IP to the company, you may want to ask the creator to confirm that the creator is in fact the lawful owner of that IP. If there is any doubt as to the true owner of the IP, an indemnity provision is one way the company can use the IP while being protected from any claims that the IP breaches copyright, trademark, or other IP laws.
If an indemnity is provided, the company can demand that the creator pay all damages and legal fees arising from anyone making a claim that they are the true owner of the IP and that the company is using the IP without their authorization.