Your cake mark. Alas, your current choice of mark creates a couple of challenges: (1) 'cake' is thegeneric term that describes what you make so you'll likely have to disclaim that (which means you can't claim any rights in "cake" by itself); and (2) the use of an owner's personal name is generally considered by the USPTO to be descriptive. That means if you want to register it on the Principal Register (the federal trademark register that has the most value), you'll need to demonstrate secondary meaning -- that is, that cake consumers associate your trademark with your cakes. For example -- if we can digress to ice cream -- Ben & Jerry's Ice Cream has become so well known that it has acquired secondary meaning and is entitled to trademark protection. If you haven't started using the trademark, secondary meaning is difficult to prove.
More about personal names. Sometimes an applicant with a personal name mark will not have to prove secondary meaning if additional wording is used with the name, but that's not the case when the additional wording is a generic term like cake (check out this decision). We know that the rules describe surnames (family names) but the first and middle names you are using can also be confused with common first names and family names and we think it will still trigger a letter of objection from a trademark examiner.
What can you do? You can file your application for registration on the Supplemental Register. That lets you use the 'R' in the circle and claim other rights. After five years of use (or perhaps sooner if you can show secondary meaning), you can move the mark to the Principal Register. Alternatively, you can file on the Principal Register and see if the examiner objects and if so, amend your application for the Supplemental Register at no additional cost. As for the statement from the person authorizing use of the name -- that's a little tricky because you are not using the person's first and last name so it's not clear whether you are identifying a real person (especially with "cake" tossed on at the end). In any case, you can provide that statement at the time you are filing or later, as part of an amendment to your application.