I looked up in dictionaries and found that
grave. Why do Japanese people use the word
grave in their names?(e.g. 大塚 愛) Or does this character have other meanings when it's used in names?
塚 is actually a mound or small hill. 大塚 translates literally as big-mound. It so happens that some graves were built as mounds, and so 塚 also came to be used to mean grave, but I don't think it is very commonly used in that sense now. There are a few Jomon era 貝塚 (kaizuka) around Tokyo, where the Jomon people disposed of their empty shellfish shells in mounds.
There is a story about Taira no Masakado, a Heian Era figure who had his head cut off in a power struggle to become emperor. He was so angry at having his head cut off that it flew all the way from Kyoto to what is now Otemachi, Tokyo. There it remains (supposedly) under the "Taira no Masakado no kubizuka (平将門首塚)", a small mound with a memorial on top. According to local folk legend, MacArthur wanted to remove it, but the men who tried suffered a terrible fate, so it was left as it is. Rumor also has it jinxed MacArthur's chance of becoming president.
The use of kanji 塚 is mentioned in the etymology of family name 大塚 on 名字由来net. Overall text are quoted and furigana has been added for ease of reading.
In particular, look into the third last and the second last of sentences. Self-translated text follows after the quoted Japanese text.
The word is said to have originated from place with high ground that made of piles of soil or stone. Subsequently, "塚" includes meaning of grave, becomes place name and transformed into family name.
Similarly, 大塚 on 民俗学の広場 mentions that meaning of grave is otherwise known in general, which somewhat hints that the meaning of grave is secondary.
As side note, the family name 大塚 shall not be mistaken for the city name, as in 大塚 (文京区) on ウィキペディア that happened to have similar etymology but takes meaning of ancient grave as primary origin.
Above all, the kanji 塚 in Japanese family name is said to be first based on the characteristics of a place, and only later that the meaning of grave was added.