In a sense, it is equivalent to the star telling fans that this is a name specially signed for her, and the meaning will definitely be different. Generally speaking, the signature with the word to is something that has been specially processed and has special significance.
Usage of to
To can be a preposition or a structural auxiliary word. When used as a preposition, it is followed by a noun or gerund, for example, give the book to Tom. I look forward to meeting you. As for when to use, the usage of prepositions is fixed. Instead of remembering many confusing meanings, it is better to recite fixed phrases directly.
When sitting as a structural auxiliary, it is an infinitive, that is, the do form, which must be followed by the verb prototype. It can also be understood as fixed collocation, such as what you want to do and what you will do. So it's best to remember fixed phrases.
After the modal verb, add v directly instead of to. Add to do sth. Action verbs (if necessary).