If you want to write the name of a loved one in Chinese but we both have English names, what symbols would we use, bearing in mind there is no 'alphabet'? Or is there a way of spelling it out?
Writing Chinese names, that is, English names in Chinese is not an impossible task for the Chinese language. Although there is no such thing as the Chinese alphabet, the Chinese characters (or symbols) still have a pronunciation which can be used to write a word that does not exist in Chinese. To be exact, the Chinese would use an existing word, and its written character, to transcribe a foreign name.
Now how does this work in reality? As you may imagine, the Chinese read the news of the world in Chinese and when, say, Bill Gates visits China, they write his name in Chinese. They use two words which sound like "gai" and "ci" (pronounced together as "gaitsu") for his surname and "bi" and "er" (pronounced together as "beer") for his first name. So his name in Chinese is Bier Gaici (beer gaitsu). All of these 4 characters originally have a meaning but it becomes irrelevant as soon as they are used for a foreign name.
Of course, the symbols cannot be just any symbols because the Chinese prefer to pick ones with positive rather than negative meanings. But especially for writing foreign names, they tend to choose from the same relatively small set of characters, especially the ones that are known to be used in foreign names and are otherwise not in use anymore. This is especially true for names of foreign products or corporations.
Cover of Dan Brown's The Da Vinci Code in Chinese, showing Leonardo Da Vinci's name written in Chinese
So even if there is no Chinese alphabet, foreign names can indeed be written in Chinese. So you can have your name written in Chinese. Or Japanese, or Russian, or any other language. In our modern world, all languages are able to write the names of foreign politicians and rock stars.