For the "name tag" sense, Iwakoku says "今は言わない。"
Sankoku, smk, and shinsen don't have that sense either.

@@ -16,0 +17 @@
+<misc>&dated;</misc>

Tails don't wag dogs here. Our approach is to set the context in the field tags and not to repeat it in the gloss. If apps fall short, so be it.
Jisho has a forum, but in any case, I've emailed the owner/developer about this issue.

@@ -13 +13 @@
-<gloss>one's hand (when playing cards)</gloss>
+<gloss>one's hand</gloss>

Add this to the list of jisho.org quirks(well, probably not just them).  I don't know how well the [fld] tags are supported by various consumers of jmdict, but there is a danger in relying on them entirely for disambiguation. 

Usually a missing [fld] tag would just remove a little information from the gloss, so I hope not to make a major issue over this, but for a kanji beginning with "手", "one's hand" is completely ambiguous.

Besides jisho.org, weblio doesn't include the [fld] info either.  
https://ejje.weblio.jp/content/手札

JMdictでの「手札」の英訳
手札
読み方：てふだ
(1)
文法情報	（名詞）
対訳	one's hand

vs.
研究社 新和英中辞典での「手札」の英訳
てふだ 手札
〈トランプの〉 a hand

I would love if the jisho.org team were open to help in fixing some of these things, but the website disclaims any interest in contributions, and things seem fairly fixed as they are...

@@ -13 +13 @@
-<gloss>one's hand</gloss>
+<gloss>one's hand (when playing cards)</gloss>