There are some factors that need to be considered such as
- the size of the bed and consequently the size of the plants (and how many letters).
- What kind of sun exposure, watering needs (can you water this area?), what kind of soil?
- Also, remember that any plant will grow over the course of the season and in doing so will change shape (of the letters)
- your location and when first and last frost arrives (length of growing season) and how cold does it get in the winter (USDA zone)
At the simplest, you could buy short-lived bedding plants for the season, spell out your name, and in each season, replace them with something else.
(They would start out small, leaving gaps in the letters, fill out, then eventually become overgrown and/or become scraggly and die off, needing to be replaced. You could also start off densely planting them, then thinning them -- removing extras -- as they grow and overlap eachother.)
A more elaborate and long-term plan would be to plant perennial and possibly evergreen herbs or mini shrubs, nurture them to maturity, and maintain them (i.e. periodically prune them) like a knot garden.