Sorry about your loss, but what's wrong with "Sammy"? Or have it done in Hebrew.
like most people they think Chinese characters ie Kanji looks cool. Probably why OP insists he wants it done in Kanji and not in Katakana.
It's not Japanese convension to literally translate names into Kanji, imaging calling someone named Alexander or Alex 人間の保護者, just his name means "protector of man" in Greek.
I personally don't know any foreign names gets translated based on meaning into Kanji , western names have always been transcribed into Katakana based on pronunciation.
If your dog had a Japanese name, than sure Kanji would be fine (though pets still have their names in Katakata like the famous Hachiko). But your dog's name was Hebrew. If neither you nor your dog have Japanese heritage, then I think permanently inscribing your dog's name in another alien language would be both a disrespect to your dog and to the Japanese culture. Might sound hash but I certainly don't want my name to be translated and inscribed in Arabic or Russian literally when I die.
And you said Sammy mean "bright sun" in Hebrew however I just checked on Wikipedia, Sammy is a derivative of Samuel and it is Hebrew name meaning "name of God" or "God has heard".
Samuel (name) - Wikipedia, the free encyclopedia
Now the Sun, is very important to the Japanese people, as you probably tell by their national flag, heck even Japan in Japanese contain the Kanji for Sun.
There is the Kanji 日 for the Sun (this kanji can mean day, Sun and Japan and is the most used Kanji in Japanese language), the physical Sun 陽 (usually used with another Kanji) , the rising Sun 旭.
Since you want "bright sun", personally I think the best translation is still 明るい太陽, however you said that you didn't like the look of it because it contains hiragana or in your words "simple symbols", and you wanted something else without changing the meaning. I mean yeah of course, Japanese writing system was designed for the aesthetics of patterns of ink on your skin. So it seems to me that you dislike "simple symbol" ie the kana and prefer all Kanji like 明朗陽 (which also requires hiragana な inserted) yet you reject Chinese language for a tattoo.
peace out.