The wedding logo, or monogram, as other people would call it, is not so different from the rest of the logos floating around in our daily lives. It will serve as your "identity" for the wedding, threading all the experiences during that day and branding it as yours. A thank you tag is just as any thank you tag until you place your monogram on it.
"A logo needs to introduce itself compellingly to the viewer in the tone and manner befitting the project or brand, whatever it may be" Adrian Clifford, Australia; Logo-Art: Innovation in Logo Design by Charlotte Rivers.
In this case, that project or brand is you, the couple. It may be as simple as two letters stuck together, but oddly, it's compelling enough for you (and other people) to realize that yes, it is you. I would always recommend to people to always stick with one logo. If two, they need to be variations of the same thing. Because really, you can't even imagine Coca-Cola having two logos.
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