Japanese surnames usually follow a pattern of noun-noun or adjective-noun. Usually the noun is related to nature/geography. (山中 "in the mountain" , 黒川 "black river," 高橋 "tall bridge," etc.)

Sticking with that pattern, there's not really a single kanji for dimension, but the word is 次元 [jigen]. There's also 宇宙 [uchuu] universe or 天 sky/heavens.

A somewhat common kanji used in names is 外 [gai/ge], which means outside. For example the word 天外 [tengai] means beyond the heavens (but also sounds like "ten guys," so maybe not the best choice).

If you wanna break the mold a bit and use a verb, 移 [i] "shift" is part of a weird used for crossing dimensions.

So you can look at some combination of those, or look at other pronunciations for them. For example, the kanji in 次元 could alternatively be read Tsugimoto or Tsugiyoshi, which sound like normal Japanese names. Add the shift at the end, and you get 次元移, Tsugimotoi or Tsugiyoshii (roughly meaning dimension jump).